Marinate the Chicken: In a bowl, combine the chicken breasts with 3 tablespoons olive oil, 3 tablespoons balsamic vinegar, and 1 teaspoon garlic powder. Marinate for at least 30 minutes (or up to 2 hours) in the refrigerator.
Grill the Chicken: Heat a grill to medium-high heat. Grill the chicken for 5-6 minutes per side, or until cooked through and no longer pink in the center. Let the cooked chicken rest for a few minutes before slicing it thinly.
Prepare the Salad: In a large bowl, combine the chopped lettuce, onion, cucumber, and chopped tomato.
Make the Dressing: In a separate small bowl, whisk together 3 tablespoons olive oil, 3 tablespoons balsamic vinegar, 1 teaspoon garlic powder, and the juice of 1 lemon. Season with salt and pepper to taste.
Assemble and Serve: Add the sliced grilled chicken to the salad. Pour the dressing over the salad and toss to coat. Crumble the feta cheese on top.
Serve immediately.