Stir together the rice, 1 1/2 cups water, and salt in a saucepan over medium-high heat and bring to a boil.
When water begins boiling cover the pan and reduce the heat to low. Simmer over low heat, WITHOUT REMOVING THE LID, for 10 minutes.
Turn off the heat and let the rice sit on the stove, KEEPING THE LID ON, while you make the chicken.
MAKE THE CHICKEN:
Add the tomatoes, onion, serrano, and garlic to a food processor or blender and pulse until everything is finely chopped.
Heat the peanut oil in a large saute pan over medium-high heat. When the oil is hot add the tomato mixture to the pan and cook, stirring often, for about 5 minutes.
Stir in 1 tsp salt, 1/2 tsp black pepper then lay the chicken breasts in the pan and bring to a boil.
When the liquid in the pan begins boiling cover the pan and reduce the heat to medium-low.
Simmer, while covered, over medium-low heat for about 10 minutes.
Flip the chicken breasts over then place the lid back on the pan and simmer until chicken is cooked through, 10 to 15 more minutes.
When the chicken is cooked transfer the chicken to a serving plate and set aside leaving any sauce in the pan.
Stir the peanut butter into the sauce and simmer over low heat, stirring often, until well combined and heated through, about 5 minutes.
Taste the sauce and season with additional salt & pepper as needed. Pour the sauce over the chicken and serve with the steamed rice.