Heat a grill pan over medium-high heat. Sprinkle chicken evenly with 1/4 teaspoon salt and 1/4 teaspoon black pepper. Add chicken to pan; cook 6 minutes on each side or until done.
While chicken cooks, heat a small saucepan over medium heat. Add oil to pan; swirl to coat. Add remaining 1/4 teaspoon salt, remaining 1/4 teaspoon black pepper, onion, and next 5 ingredients (through jalapeño); cook 8 minutes or until vegetables are tender, stirring occasionally.
Place tomatillo mixture in a blender; add lime juice. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Pulse 10 times or until a chunky salsa forms. Spoon tomatillo mixture over chicken; sprinkle with cilantro.