Trim chicken of any excess fat or sinew. Slice, across grain, into 3 by 1/2 inch strips. Stir marinade ingredients together in a medium bowl. Add chicken strips and toss to evenly coat. Set aside at room temperature, uncovered, 30 minutes. It's important not to marinate any longer, or the acid in the lemon will break down the fibers of the chicken.
Meanwhile, prepare the salad. Whisk together olive oil, lemon juice, salt, and pepper in a bowl. Tear watercress into bitesized pieces and toss with dressing. Divide salad among 6 serving plates. Thinly slice avocado halves into strips lengthwise and arrange on salad. Reserve in refrigerator.
To cook chicken, heat a large dry cast iron skillet over high heat 15 minutes. (Yes, 15 minutes.) Heat peanut oil for frying. Lift chicken strips from marinade, one at a time, and add to pan, standing as far away as possible to avoid splatters. Fry until dark golden brown and crisp, about 1 minute per side. Arrange about 8 hot chicken strips on each salad in a spoke pattern. Serve immediately.
c.1997, M.S. Milliken & S. Feniger, all rights reserved