Combine chicken, oil, lime juice, and garlic in a bowl. Refrigerate for 30 minutes. Preheat a grill or grill pan to high. Grill chicken until cooked through, about 4 minutes per side.
Combine greens, mint, and radishes. Sprinkle with salt, season with pepper, and drizzle with oil and lime juice. Serve with chicken and lime wedges.
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