Heat the oil in a large soup pot or Dutch oven (5-6 quarts) over medium heat.
Once hot, add the onion, peppers, garlic and 1 teaspoon salt. Sauté, stirring often, until the vegetables have softened, about 8-10 minutes.
Push the vegetables to the edges of the pan and add the tomato paste directly onto the center of the pot's surface. Sauté, stirring occasionally, until the paste darkens in color, about 2-3 minutes (this helps develop the flavor). Then stir the paste into the vegetables.
Push the vegetables to the edge of the pan again. Add the chili powder, coriander, cumin and paprika and saute for about 30 seconds (this also helps develop the flavors and is called "blooming" the spices), then stir into the vegetables.
Add the broth, tomatoes and chicken, making sure the chicken is submerged in the liquid. Turn the heat to high and once the soup reaches a boil, reduce the heat to bring it down to a simmer. Let it simmer for about 10-15 minutes, until the chicken is cooked through.
Remove the chicken to a cutting board. You can either cut it into bite-sized pieces or shred with two forks. Stir the chicken and any accumulated juices on the cutting board back into the soup.
Taste and adjust any seasonings. Turn off the heat and serve with your favorite toppings.