Place chicken breasts in a saucepan and cover with water. Bring to a boil over medium heat, then simmer until no longer pink, 10 to 12 minutes.
Transfer chicken breasts to a bowl. Allow to cool briefly, then shred with 2 forks.
Heat vegetable oil in a saucepan over medium heat. Add onion and cook until translucent, 2 to 3 minutes. Stir in shredded chicken, tomato sauce, cumin, and chili powder. Bring to a boil, then reduce heat to low and simmer until chicken is hot and flavors have blended, about 3 minutes.