Thread venison, onion pieces, and pepper pieces alternately onto 4 (15-inch) metal skewers.
Combine chutney and next 3 ingredients in a small bowl; stir well. Brush mixture evenly on kabobs.
Coat rack of a broiler pan with cooking spray. Place kabobs on rack; broil 5 1/2 inches from heat (with electric oven door partially opened) 8 to 10 minutes or to desired degree of doneness, turning occasionally.