Rinse the shrimp under cold running water. Dry the shrimp with paper towels and toss them in the oil to coat. Season with 1-1/2 teaspoon salt.

Prepare a medium-high gas or charcoal grill fire. When the grill is ready, use long-handled tongs to put the shrimp on the cooking grates, arranging them across the grates so they don't fall through. Grill, turning halfway through cooking, until the shrimp curl and become pink, 2 or 3 minutes per side. Transfer to a platter. Serve immediately with the dipping sauce of your choice, or chill to use in a seafood salad or a cold shrimp cocktail.