1. Preheat grill to 300° to 350° (medium) heat. Brush both sides of onion and mangoes with olive oil. Grill onions, covered with grill lid, 5 to 6 minutes on each side until softened and grill marks appear. At same time, grill mangoes 2 to 3 minutes on each side or until softened and grill marks appear. Remove from grill; cover and let stand 15 minutes.
2. Meanwhile, bring vinegar and next 4 ingredients to a boil in a small saucepan over medium-high heat. Reduce heat to low, and simmer 5 minutes. Add jalapeño, and simmer 5 minutes. Remove from heat; transfer to a bowl.
3. Chop onion and mangoes, and stir into vinegar mixture. Stir in cilantro and lime juice. Serve chutney warm or at room temperature.