Chicken Chili?

Can I use ground chicken breast the same way I'd use ground beef in chili con carne? Do I want to?

I've been making this recipe for years, substituting ground turkey - or in your case, ground chicken - the concept is the same, however, you must change your approach. You'll want to build the flavors sans meat to avoid a dry chili, adding the meat at the end just until it's cooked through and has had a chance to reduce a bit.

Turkey Chili
Preparation time: 20 minutes
Cooking time: 25 minutes
Yield 8 servings

3 tablespoons olive oil
¼ cup salt pork, diced
¾ cup onion, medium dice
1 red pepper, medium dice
1 poblano chili, medium dice
½ teaspoon salt
freshly ground pepper
3 cloves garlic, minced
3 tablespoons chili powder
¼ teaspoon each, cayenne, cinnamon, cumin
3 tablespoons tomato paste
1 ½ pounds ground turkey
1 14.5 ounce can diced tomatoes
½ cup cilantro, chopped

Heat olive oil in large skillet over medium heat. Render salt pork until just crispy, about 5 minutes. Stir in onion, pepper, poblano, salt and pepper; cook until onion is translucent, about 3 minutes, stirring occasionally. Stir in garlic, chili powder, cayenne, cinnamon and cumin; cook 2 minutes. Stir in tomato paste and cook until paste darkens, about 3 minutes. Stir in turkey and canned tomatoes, simmer, uncovered, until liquid reduces and turkey is cooked through but not dry, about 15 minutes. Remove from heat, stir in cilantro; taste and adjust seasoning.

Serve with steamed corn tortillas
Or
Corn bread

I ate a little too much ground beef as a child so sometimes I do ground chicken or turkey and supplement with some hot italian sausage (pork) for fat/flavour.

Personally, if I had yet to buy the chicken, I'd poach chicken (either pieces or entire, and very preferably on the bone for better flavor) and shred it along the grain for a superior texture (ground and diced chicken tends to be more rubbery); I'd add it to the chili once the chili was removed from the heat.

You can although it will impart little to no flavor. The texture is different as well.

Sure you can. I use ground turkey routinely. I also add some chipotle chopped up in adobo sauce for some kick. You can use dark turkey, or white meat or a combination.