For the Salsa
In a bowl, whisk 2 tablespoons oil, lime juice, garlic paste, and salt and pepper to taste. In a non-stick skillet heat remaining tablespoon olive oil over moderately high heat, until hot, but not smoking. Saute corn until deep golden (4 minutes). Add corn and remaining ingredients to bowl and toss to combine well. (Beets may bleed slightly, coloring other ingredients).
For the Chicken
Pat chicken dry and season with salt and pepper. On a plate stir together cornmeal, paprika, and cayenne and press chicken into mixture, coating both sides. In skillet heat butter over moderately high heat until foam subsides and saute chicken until golden and cooked through, about 5 minutes each side. Serve chicken with salsa.