Using the flat side of a meat mallet, flatten chicken between two pieces of plastic wrap to 1/4- to 1/2-inch thickness.
Lightly grease a panini griddle, covered indoor electric grill, or large skillet with oil. Heat over medium heat or according to manufacturer's directions. Add chicken. If using griddle or grill, close lid and cook 4 minutes or until no longer pink (165 degrees F). (If using skillet, cook 8 minutes, turning once.)
Arrange chicken and next five ingredients (through fennel) on plates. Drizzle with Champagne Vinaigrette.
In a small bowl, whisk together grapefruit juice, champagne vinegar, olive oil, salt, and ground black pepper.