In a small bowl, combine 2 tablespoons olive oil, lime zest and juice, and honey. Add salt and fresh ground pepper to taste.
Place the cubed watermelon in a bowl. Drizzle with 2 teaspoons of the dressing and toss to coat. Refrigerate until ready to use.
Place each chicken breast between two pieces of plastic wrap. Using a rolling pin/mallet/whatever heavy item you have on hand, pound the breasts to approximately ¼-inch thickness. You want these really thin, peeps, but please be careful not to tear them. Season the chicken on both sides with salt and pepper.
Heat a large cast iron skillet over high heat. When hot, pour in ½ tablespoon of olive oil and swirl to coat the bottom of the pan. Add one of the chicken breasts to the pan and cook for 2 minutes on each side until opaque throughout and lightly browned. Transfer the chicken to a plate, add the remaining ½ tablespoon olive oil, and cook the second breast.
Toss the arugula and red onion with the remaining dressing. Add the marinated watermelon and toss again.
Top each chicken breast with half the salad and sprinkle with feta cheese. Serve immediately.