Heat the oil in a large nonstick saucepan over medium-high heat.
Add the garlic, celery, bell peppers, jalapenos and onions and sprinkle over the salt. Cook, stirring occasionally, until the vegetables are tender, about 8 minutes.
Add the chicken, breaking it up with a wooden spoon, and cook until it starts to brown. Stir in the chili powder and cumin and cook until the chicken is fully browned, about 6 minutes.
Add the tomatoes, kidney beans and pinto beans and bring to a boil. Reduce the heat and simmer, covered, stirring occasionally, until the flavors are blended and the chili begins to thicken, about 1 hour.