All chocolates today have back of them an early English dog, Buccleuch Avon (whelped 1885). He was a black dog but carried the chocolate (or "liver") color gene. Almost all chocolates today got the gene through another British dog, Dual Ch. Banchory Bolo (whelped 1915), who also passed along the interesting trait of a large white spot just behind the big paw pad on the front paws. These are still known as "Bolo spots", and my chocolate has faint ones.
The gene for chocolate/liver color is separate from the gene for a yellow coat. Basically, the yellow recessive gene is like a switch that turns off the HAIR pigment (but not the SKIN pigment). If a dog has two of the yellow genes, he'll be a Black Lab with a yellow coat. EXCEPT if his parents happen to throw the chocolate gene . . .
Then what you get is a Chocolate Lab, but with the hair pigment turned off. So you get a somewhat odd looking dog with the brownish-pink skin (especially the nose, paw pads, and eye rims) of a chocolate but a yellow coat. This is called a "Dudley" by the show people - not to be mistaken for a regular Yellow Lab who has "snow nose" - fading pigment in cold weather.
A Dudley is disqualified from the show ring, and that's the real reason the Chocolate Lab is the rarest - most show people didn't want them in their bloodlines for fear of having a Dudley crop up. That's also why people say that chocolates are crazier or more hyper or wilder than blacks or yellows -- it's just because most of them have been bred by field people who are looking for a higher energy dog.
Now the show folks are breeding chocs, but they keep their choc and black lines separate.