Whisk together lemon juice, minced garlic, freshly grated ginger, thyme, salt, and pepper. Using a knife, make a few small slits in each chicken breast and then place them in a large baking dish. Pour lemon marinade over the chicken, cover dish, and refrigerate for one hour.
Meanwhile, cook rice as directed on package and steam broccoli.
Spray a large skillet with cooking spray and heat over medium. Add chicken to skillet, reserving marinade. Cook chicken 5-6 minutes on each side until no longer pink in the center.
Add marinade to a small sauce pan and boil for 5 minutes, stirring frequently.
Top rice with chicken and drizzle with marinade. Serve broccoli and grapes on the side.