In a medium pot, add chicken and cover with 1 inch of water. Add 1 tablespoon of salt. On medium-high heat, bring water to a roaring boil. Remove from heat and cover tightly for 30 minutes or until there's no longer any pink in chicken. Remove chicken from pot, let stand until cool enough to handle, then dice.
Sautee onion, red pepper, and jalapeno in a large pot until very soft. Add garlic and saute for 2 minutes. Add salt, black pepper, chili powder, oregano, smoked paprika, and cumin. Saute for about 1 minute.
Add all the rest of the ingredients except for the chicken. Simmer on medium-low heat for 1 1/2 hours to allow all the flavors to develop. Add water, as needed, to the soup if it gets too thick. Add chicken and heat through. Garnish soup with cilantro, tortilla chips, and cheese. This soup is even better if made and refrigerated a day ahead of serving.
If you are in a hurry, don't worry about the simmer time. The soup is still wonderful if you heat everything through after you saute the veggies. I like the long simmer because I like the canned veggies to soften and the flavors to really merge.