Heat grill to medium; lightly oil grates. In a shallow dish, stir together 2 tablespoons lime juice and garlic; season with salt and pepper. Add chicken and coat. Let sit 15 minutes.
In the bowl of a food processor, pulse onion and jalapeno until finely chopped. Add tomatillos and pulse once or twice. Fold in tomatoes, cilantro, and remaining lime juice; season with salt and pepper.
Grill chicken, covered, until opaque throughout, about 10 minutes per side. Transfer to a plate and tent with aluminum foil; let rest 5 minutes. Serve chicken with salsa.