1) Combine lime juice, olive oil, lime zest, garlic, thyme, and salt and pepper. Marinade chicken in this mixture for at least 30 minutes, but many hours or overnight is better.
2) You can grill these breasts or heat an oven-safe skillet over medium-high heat. Once hot, add a drizzle of oil and cook the breasts for about 4 minutes per side. Then transfer chicken to the oven to finish at 350 degrees F. for 15 minutes. Check doneness by carefully cutting into one of them or using a meat thermometer. You are shooting for 165 Degrees F in the thickest part of the chicken.
3) For the pico, dice up everything very fine and stir together. Season with salt and pepper to your taste. If you can make this a few hours in advance it will be much better.
Serve chicken with lots of fresh pico and rice. Or slice and make tacos?