I heard that a lot of GM's prefer the kids to be at least 7 years old. I can't recall where I read that (was a while ago), but to answer your question: yes, 8 should be a great age to teach your kid chess.
Just remember to respect your child's decision if he/she doesn't enjoy the game at all ;)
(Looks like my son is going to be into cars... I know nothing about them...)
I learned when I was about 8 I think. Of course, temperment and patience has a lot to do with it. A calm, (relatively) patient 6 year old will be a better student than a hyper, can't stay sitting down 9 year old.
i am teaching my 5 year old the basics, i highly recommend a game called no stress chess. its a combonation card/chess game. you have pictures of where the pieces go on one side of the board and you draw cards to see which piece you are allowed to move. then when they get better you can draw three cards at a time and you get to choose which one to move. then on the opposite side is a regular chess board with grid markings. he loves it and already knows where to place the pieces(usually) and understands some of the basics.
I think you should teach a child when they show real interest. I had a small cousin that only wanted to used the pieces like dolls. He was not interested in learning how they move on the board.
IMO, around eight or nine is a good age to learn. Nine is when I learned. OTOH, some kids start playing before kindergarten. It all depends on the maturity of the kid. If they can grasp the ideas then I say teach them.
The Chester and Fritz games are pretty good. My five year old knows the moves and can play a game. My eight year old understands tactics a bit better, the younger one can on;y think one move ahead 
Eight is fine, most of the greats started even earlier. I think it's fine to teach them as soon as they are old enough to express an interest... where's the harm? it's not like you are teaching a kid to shoot or throw a knife, is it?
Yes, definitely 8 years old is a great age to start playing chess, but a person as young as 5 can easily learn if they show a lot of interest in the game and you can find ways to make it more fun for them. The school where my daughter attends started an after school chess program for Kindergarten through 2nd grade. She started when she was 7. She would much rather play with kids her own age than with me though. If I didn't try to make it a little bit easy for her to beat me at first, she got upset, but now I have to be careful to keep it challenging for her as she has improved both her defense and attack strategies susbstantially. If you aren't already aware of it, chess.com has a site named chesskid.com that is designed especially for younger players. I'd recommend it if your child enjoys the game.
I learned the moves when I was 6 but I didn't really learn anything tactically at all until I was 8 and I didn't start to "study" (if you can even call it that) until I was 15. But yes 8 is fine. My father's strategy for teaching me was after I learned the moves he would attack me with 1. e4 e5 2.Qh5 and go for a scholar's mate (or a delayed scholar's mate) again and again until I could defend it... I got frustrated 
My 4yo son already knows how to set up the pieces and he loves to move the pieces, some totally randomically, and hit the clock . Chessmaster 10th edition fun section totally hooked him. I think the key at this age is just have fun and don´t stand strictly by the rules. Let him have a nice trip!
Today I gave a chess set to my 9yo nephew as a birthday gift and managed to teach him some basics. He didn´t feel like was having a good time. Another 9yo kid who was watching us seemed to be very interested and started asking questions and making conclusions. If properly guided that kid may go further.
"My 4yo son already knows how to set up the pieces and he loves to move the pieces, some totally randomically, and hit the clock"
That made me smile.
you should be at least 30 years old before you start teaching a child.
... of course, it is not related exactly to age, but rather to a combination of maturity, temperament, analytic ability, patience, etc.
But, is it ok to try and teach my 8 year old how to play chess?
Why on EARTH would it not be okay to teach somebody chess just because they were eight years old?
... of course, it is not related exactly to age, but rather to a combination of maturity, temperament, analytic ability, patience, etc.
But, is it ok to try and teach my 8 year old how to play chess?
there's no one-fits-all age.
"My 4yo son already knows how to set up the pieces and he loves to move the pieces, some totally randomically, and hit the clock"
That made me smile.
+1
Children should not learn chess!
Let them grow up to be Physicists, Mathematicians, Engineers, Artists, anything but a worthless Grand Master chess palyer at the age of 21! Chess is a waste of time and there is no money in it: it is a hell of way to try to live as a Professional Chess player.
I figure, when somebody is about 60 years old, that it the time to learn Chess!
I taught mine at 4.
There were two gimmicks I used, after I figured out that he knew the basic moves.
First, when he and I played, I used a chess clock set for one minute. If I won, I added one minute for our next game. If I lost, I subtracted one minute. I did not make the moves as fast as possible. I took several seconds per move every time.
At first, what that meant is that I tried the "scholar's mate" every game. If he fell for it, I won. Otherwise, I lost if I had one minute. For a long time, I could usually win in two minutes even if he didn't fall for the scholar's mate. We didn't play tons of chess, but by age six, I was getting five minutes, and he was winning six year old tournaments, unrated, at his school Chess club.
The other gimmick was a computer program called Majestic Chess. Highly recommended for teaching small children, if you allow them to use a computer for game play of any sort. It's basically a chess themed puzzle and adventure game, where you solve Chess puzzles to earn gold, which allows you to buy magic items like the Hammer of Bishop Striking.
Now, "should" you teach your child Chess? For me and my son, Chess is a game. One game out of many. I had already taught him Checkers. My father taught him Hearts when my son was six, and my father passed away the next year. It's one of my kid's great memories of his grandfather. I have since taught him Shogi and Xiangqi, Blokus and Cribbage, Magic: the Gathering and Star Fleet Battles. I think teaching kids games is great. However, my son is not an avid Chess player. He plays in tournaments, but his rating has dropped below 500, and that doesn't bother him a bit.
If you want him to be "good" at Chess, I think you should hold off until 8 or 9. He can't take it seriously before then, and if he starts out not taking it seriously, he might never take it seriously.
"My 4yo son already knows how to set up the pieces and he loves to move the pieces, some totally randomically, and hit the clock"
That made me smile.
Reminds me of my little sister. She would scribble all over a piece of paper then run up to our mom and proclaim "look mommy! I can write in cursive!"
Not quite as good of an image though as your story
+2
... of course, it is not related exactly to age, but rather to a combination of maturity, temperament, analytic ability, patience, etc.
But, is it ok to try and teach my 8 year old how to play chess?