In a small bowl, whisk together hoisin sauce, soy sauce, honey, and vegetable oil.

Place chicken breasts in a resealable plastic bag and pour half of the marinade over the chicken. Seal the bag and marinate in the refrigerator for at least 1 hour, or overnight.

Preheat grill to medium-high heat. Remove chicken from the marinade, discarding the marinade. Grill chicken for 6-8 minutes per side, or until cooked through. Remove from grill and let rest for 5 minutes.

Slice the chicken into thin strips.

In a large bowl, combine salad greens, cucumber, carrot, cilantro, peanuts, and the remaining half of the marinade. Toss to coat.

Divide the salad mixture among 4 plates and top with sliced grilled chicken. Serve immediately.