Season the chicken with salt. In a large skillet, heat the EVOO over medium-high heat. Add the chicken and cook, turning once, until golden, about 5 minutes. Add the pepper and cook, stirring, until tender, about 3 minutes. Stir in the chili sauce and honey and cook until slightly reduced.
Arrange the lettuce cups on a platter. Divide the chicken mixture among the cups and top with the peanuts, lime juice and basil.