First off you're gonna need at least two saved games.

Second you have to save the chickens in Brightwall so that you can race the chickens.

Third just bet all your money on one chicken (Mr. Cluckles seems to win the most and you win more money on him).

If your chicken loses, then pause your game before the cutscene ends and simply load your other character, this way you dont lose any money and are able to bet over and over again until you win.