Cut chicken thighs into two or three pieces per thigh, removing any large pieces of fat while doing so.
Place the trimmed thighs in a pot that holds four or five quarts.
Combine the tomato puree, onion, garlic, cilantro leaves,chili powder, salt, and pepper in a blender and puree.
Pour the puree over the chicken and place the pot over medium-high heat. Bring to a low boil and then reduce to a simmer. Cook for two to three hours, until the chicken shreds easily.
When the chicken is nearly done, start building the rest of the chili.
Heat the oil over high heat in a large Dutch oven or soup pot that will hold eight to nine quarts.
Add the onion, garlic, chili powder, and cumin to the pot and stir to the combine. Cook for four to five minutes, until the onions begin to brown and the spices are fragrant.
Add the chopped peppers and stir to incorporate.
Take the Swiss chard stems and chop into 1/2 inch slices like you would celery. Add them to the pot. Chop the greens and set them aside.
Add the tomatoes and their liquid to the pot, crushing them with your hands as you add each one.
Open beans, drain them of their liquid and add them to the pot.
Add the shredded chicken and its cooking liquid.
Finally, stir in the reserved Swiss chard greens.
Reduce the heat to medium low and simmer the chili for 30 to 45 minutes. Taste and adjust seasonings (we like a mild chili in my house, so it might not be nearly spicy enough for lots of you).
Serve with some grated cheddar cheese and a dollop of sour cream.