Place the panini pan and press over medium to medium-high heat on separate burners until they are very hot. (The pan should not be smoking, but very hot).
Drizzle each side of the chicken breasts with oil. Season the chicken with salt, pepper, oregano and rosemary on both sides.
Place the chicken breasts into the hot grill pan. Using an oven mitt, carefully pick up the hot press and place it directly onto the chicken, covering completely.
Cook 5 - 7 minutes or until chicken is thoroughly cooked.
Remove from grill pan and place on a tray to rest. Cover loosely with aluminum foil.
While chicken is resting, cook the vegetables.
Place the vegetables on a tray, drizzle with oil and season with salt and pepper.
Place the vegetables into the hot grill pan and cook about 1 - 2 minutes, turning once.
Remove the vegetables from the grill pan and drizzle the asparagus with lemon juice.