Place a medium non-stick pan over high heat. Add 1 tsp. olive oil and pineapple chunks to hot pan. Stir often until charred, 3-4 minutes. Transfer to a plate and allow to cool. Wipe pan clean and reserve.
Make the Rice
Bring a small pot with 1½ cup water and rice to a boil. Reduce to a simmer, cover, and cook until tender, 18-20 minutes. Remove from burner, fluff rice, and keep covered. While rice cooks, stem and mince Fresno chile. Discard seeds if you prefer less spice. Stem half the cilantro. Mince remaining whole cilantro and stems. Halve lime. Quarter one half and juice remaining half. Halve tomatoes. Drain and rinse black beans.
Make the Salsa
Cut cooled pineapple into ¼" dice. In a mixing bowl, combine pineapple, Fresno chile (to taste), minced cilantro (reserve whole leaves for beans), 2 tsp. lime juice, and a pinch of salt and pepper.
Cook the Chicken
Return pan used to char pineapple to medium-high heat and add 2 tsp. olive oil. Pat chicken breast dry, and season both sides with ¼ tsp. salt and a pinch of pepper. Add chicken to hot pan and cook undisturbed, 3-4 minutes. Flip, lower heat to medium, and cook until chicken reaches a minimum internal temperature of 165 degrees, 3-4 minutes. Remove chicken to a plate and rest 3 minutes. Reserve pan; no need to wipe clean.
Cook the Beans
Return pan used to cook chicken to medium-high heat. Add 1 tsp. olive oil and grape tomatoes to hot pan and cook until tomatoes are lightly charred, 1-2 minutes. Add beans and cook until warmed, 1-2 minutes. Remove from burner and sprinkle on queso fresco and cilantro leaves.
Finish the Dish
Place rice on a plate. Add beans and chicken. Top with chicken with pineapple salsa.