Slice each chicken breast horizontally to create thinner cutlets. Season both sides with salt, pepper, chili powder, garlic powder, and cumin.
Heat 1 tbsp olive oil in a large skillet over medium-high heat. Cook the chicken 4–5 minutes per side until golden and cooked through (165°F / 74°C internal temperature). Remove chicken from the skillet and set aside.
Add cilantro, garlic, jalapeño, lime juice, mayonnaise, olive oil, salt, and pepper to a blender or food processor. Blend until smooth. Add 1–2 tbsp water if needed to reach a pourable consistency.
Place the cooked chicken on plates and spoon the cilantro lime sauce over the top. Serve extra sauce on the side.