Pierce each chicken breast several times with a fork. Place the chicken in a large glass baking dish or re-sealable plastic bag.
In a medium bowl, combine the tequila, ½ cup of lime juice, water and agave; stir well and set aside.
Using an immersion blender or small food processor, blend the remaining ¼ cup of lime juice, garlic cloves, cilantro, salt, and pepper until smooth. Transfer the cilantro puree to the bowl with the tequila; stir until well combined.
Pour the marinade over the chicken breasts. Cover and place in refrigerator overnight (minimum 6 hours).
Preheat an outdoor grill to medium heat. Remove the chicken breasts from the marinade and discard excess marinade.
Grill chicken until done, flipping only once. (This should take approximately 6-7 minutes per side.)
If you don’t happen to have agave syrup, you can substitute 2 Tbsp of honey or 1 Tbsp of sugar instead.