Place the olive oil in a large soup pot over medium heat. Add the onion and garlic and cook, stirring, until softened but not brown, about 3 minutes. Add the chicken broth, chili beans, black beans, corn, tomatoes, chicken breasts, and taco seasoning, and stir to combine. Increase the heat to medium-low and let the soup simmer, covered, until the chicken has cooked through, 40-45 minutes. Remove the pot from the heat and transfer the chicken to a plate to cool for 15 minutes.