Season chicken on both sides with salt and pepper.
Stir together vegan, soy-free mayonnaise, lime zest and garlic.
Coat chicken with marinade and allow to sit for at least 30 minutes or up to 10 hours in the fridge (bring to room temperature before cooking).
When you're ready to cook, preheat the grill.
Grill chicken until juices run clear and a meat thermometer reads 165 degrees, about 5 minutes per side.