Heat broiler or prepare grill with hot coals.
Finely chop drained artichoke hearts in food processor or by hand. Transfer to small bowl. Add salsa and 1 tablespoon of the reserved marinade. Season to taste with salt and pepper.
Pound chicken breasts between sheets of plastic wrap to uniform thickness of about 1/2 inch. Brush lightly with some of remaining artichoke marinade.
Broil or grill 4 inches from heat until browned and no longer pink in center, 2 to 3 minutes per side. Serve chicken topped with artichoke salsa.