Make salsa: In a bowl whisk together 1/4 cup oil, lime juice, and garlic paste, and season with salt and pepper, to taste.
In a non-stick skillet heat remaining 2 tablespoons oil over moderately high heat until hot but not smoking and saute corn, stirring, until deep golden, about 4 minutes. Add corn and remaining salsa ingredients to the bowl and toss to combine well. (Beets may bleed slightly, coloring other ingredients.)
Make chicken: Pat chicken dry and season with salt and pepper. On a plate, stir together cornmeal, paprika, and cayenne and press chicken into the mixture, coating both sides.
In the skillet, heat butter over moderately high heat until foam subsides and saute chicken until golden and cooked through, about 5 minutes on each side. Serve chicken with salsa.