In a large bowl, mix together all the ingredients, except the fish, greens, chaat masala, and lime wedges. Add the fish and mix, making sure all the pieces are well-coated. Cover with plastic wrap and marinate in the refrigerator, at least 4 and up to 12 hours.
Preheat the grill to medium-high (375°F to 400°F) or place a grill pan over high heat. Baste the grill or grill pan with oil to prevent the fish from sticking to the grill. Then place the marinated pieces on the grill or in the grill pan and cook, turning once or twice, until the fish pieces are opaque and just flaky inside and lightly charred on the outside, 5 to 7 minutes.
Line a plate with greens, and transfer the fish to rest on the greens. Sprinkle the chaat masala on top, and serve hot with lime wedges on the side.