Cut pineapple crosswise into 6 slices, each about one inch thick. Brush cut surfaces of pineapple slices lightly with oil; sprinkle with salt and pepper.
Grill over medium coals about 8-10 minutes, until golden brown, turn and grill other side to brown.
Meanwhile, combine molasses, butter and lime juice in small saucepan and heat together over low heat, stirring, until butter is melted. Remove pineapple slices from grill, brush with molasses-lime butter and serve.