Chili and cornbread were both economically viable food options for people in the American Southwest, particularly along the cattle trails that ran from Texas to Kansas. Corn meal, which is used to make corn bread, was a cheaper and more readily available resource than wheat flour, while beef was plentiful. The influence of Mexican culture informed the preparation of the meat, so the two food stuffs came together to produce the (very delicious) combo that's come down to the present.