In a shallow baking dish, whisk together the lime zest, lime juice, olive oil, honey and cilantro with a pinch of salt. Briefly set aside.
Place each chicken breast between two pieces of plastic wrap. Using a rolling pin or tenderizer (or random heavy object), pound the chicken until about ½-inch thick. This process is sort of noisy, but also cathartic. Just go with it.
Place the pounded chicken breasts into the baking dish, and make sure each one is well coated in marinade. Press plastic wrap on the surface of the chicken and refrigerate for at least 20 minutes. (Obviously, the longer you can let your chicken marinate, the better.)
While your chicken is marinating, place all the ingredients for the salsa in a medium bowl. Gently mix the ingredients with a fork (you don’t want to smoosh your strawberries), and season with salt to taste. Cover and refrigerate until ready to use.
Heat a clean, lightly oiled grill or grill pan over medium-high heat. Remove the chicken breasts from the marinade and pat them dry. Season both sides of each breast with kosher salt and coarse black pepper.
When the grill/grill pan is hot, add the chicken and cook for about 3½ minutes per side until grill marks appear and chicken is just cooked through.
Remove chicken to a plate and serve with strawberry-jalapeño salsa.