Mix the marinade ingredients together and add the chicken, turning to coat it on both sides. Marinate for 20 minutes.
Heat a cast-iron skillet on high, and add 1 teaspoon of olive oil. Place marinated chicken in the skillet. Cook, turning once, about 10 minutes total. Remove from heat.
Arrange lettuce in a large serving bowl, and top with the peaches, cucumbers, avocados, red onion and cherry tomatoes.
Whisk together the dressing ingredients in a small bowl. To serve, slice the chicken against the grain and place on top of the salad. Toss with the dressing and season with salt and pepper as needed.