Wash and dry all produce. Core and seed poblano, then cut into 1/2-inch squares. Zest 1 tsp zest from lime, then cut into quarters. Cut chicken into 1/2-inch pieces.

Heat a large drizzle of olive oil in a large pan over medium-high heat (use a nonstick pan if you have one). Add chicken and season with salt and pepper. Cook, stirring occasionally, until lightly browned, about 2 minutes.

Add poblano to pan with chicken. Continue cooking until chicken is cooked through and poblano is softened, about 5 minutes more.

Meanwhile, core, halve, and dice tomato. Place in a medium bowl and set aside. Once chicken and poblano are done cooking, stir 2 TBSP salsa into pan. Add remaining salsa to bowl with tomato and stir to combine.

Wrap tortillas in a lightly dampened paper towel and microwave until warm, 30-45 seconds. In a small bowl, stir together sour cream, lime zest, and 1 tsp lime juice.

Divide chicken and poblano mixture between tortillas. Spoon salsa and crema over top. Sprinkle with cheese. Serve any remaining lime quarters on the side for squeezing over.