Most of the chili-contest winners whose recipes have been posted online seem to use either beef chuck or tri-tip. I made a batch recently using tri-tip that came out very well. I usually add some pork shoulder also, about a third of the amount of the beef (i.e., if I use 3 lb. of beef, I'll put in one lb. of pork). Sometimes leg of lamb, or venison if I have it (up to about a quarter of the total amount of meat).
I use tri-tip beef, cut into small pieces or coarse ground.
The tri-tip beef roast or steak is located at the bottom of the beef sirloin. This cut usually weighs one and a half to two and a half pounds. This cut is also called a triangle roast. You may have to ask your butcher for this cut of meat.