Combine chicken with 2 tablespoons each oil and lemon juice. Marinate in refrigerator for at least 1 hour (or up to 3).
Stand an ear of corn on one end, and using a serrated knife, cut off kernels; repeat (you should have 1 cup total).
Heat 1 tablespoon oil in a skillet over medium heat. Add corn, chiles, and ginger, and cook until softened, 3 to 4 minutes. Let cool.
Preheat grill to medium. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 5 to 6 seconds.) Grill chicken, flipping once, about 5 minutes per side. Remove from heat.
Stir together beans, onion, corn mixture, lime juice, and 1 tablespoon oil. Add tomatoes and avocados. Season with salt and pepper, and stir gently to combine.
Toss arugula with remaining 2 teaspoons each oil and lemon juice.
Divide arugula among plates, and top with chicken and avocado-corn salsa.