I want to make chili using a ham bone (with a little meat on it). How should I cook it to make good use of both the meat and the bone?
If you're going to simmer your chili for a long time, just throw it in there. If you made stock with it, you'd still be just simmering the bone for a long time to extract the same flavors. (I'm not advocating not using stock here, just that I wouldn't make stock for the sole purpose of getting flavor out of the bone. Use the stock you would otherwise.).
Simmer four plus hours and then pull the bone out, tap the meat off, and enjoy the chili (although I like to cool chili down, put it in the fridge, and eat it the next day better).
If you're going to make the stock with it though, @Cos definitely has the right idea with the pressure cooker.
I would make a stock with it and use that for a portion of your liquid in the chili. toss it in a big pot of water with some chunks of aromatic vegetable (onion, celery, carrot, garlic) and whole herbs (thyme & rosemary) and spices (i'd do cracked black pepper and 4 or 5 whole allspice pods) and cook for 2-4 hours. strain all the chunks out and use the liquid.
if you don't want to go through all that, you could probably also just drop the bone into the chili pot and let it all cook together. just remember to take the bone out of the pot before serving. unless you're into that kind of thing.
I am guessing that you are thinking of a "Green Pork Chili" along the lines of this recipe.
IF so, the best use for your ham bone is to make a pork stock to substitute for the chicken stock. I would put the bone, with about 6-7 cups of water into a pressure cooker and use the pressure to extract all of the flavor that the marrow has to offer. 15-20 minutes under pressure should leave you with a clean bone and pot full of juices. Strain out the bits using a cheese cloth and boil the broth till you have the required volume (5 cups in the case of the recipe I linked to) and go forth from there.