Pinkie,
Most chili recipes call for beef chunks or hamburger.
My recipe calls for both.
I use "stew beef" for the chunks, and it is indeed tough if not cooked long enough. So, IMO, your thought that it might be overcooked is backwards.
I stir fry it in the bottom of the stew pot to brown it, then take it out, put the other ingredients in, and add the meat back in. The longer you simmer the chili, the more tender the meat gets.
You could always substitute filet mignon for the stew beef.
As far as cooking a meatless chili, I don't see why you couldn't use beef bouillon to add some meat flavor and omit the meat, or use all hamburger and omit the meat chunks.
Let us now how it turns out.
Phil
P.S. BTW, real chili doesn't have beans in it, but I like some in mine.