Whisk 1 tablespoon olive oil, lime juice, 1 teaspoon salt, and 1/2 teaspoon pepper in 11x7-inch glass dish. Add chicken and turn to coat. Marinate 30 minutes, turning occasionally.
Prepare barbecue (medium-high heat). Whisk remaining 4 tablespoons oil, 1/2 teaspoon salt, 1/2 teaspoon pepper, onions, shallot, vinegar, thyme, and mustard in large bowl to blend. Mix peaches, avocado, and radicchio into dressing; toss to coat.
Grill chicken until cooked through, about 5 minutes per side. Transfer to work surface; cut crosswise into thin slices. Mix baby greens into dressing in bowl. Divide salad among 4 plates. Arrange chicken alongside and serve.