Start by soaking the bamboo skewers in a shallow dish filled with water for 30 minutes. (Do not skip this step people, or your skewers will catch fire on the grill, which is terrifying.)
In a small bowl, whisk together the soy sauce, lime juice and zest, honey and Sriracha. Briefly set aside.
Slice your chicken breasts into approximately 1-inch chunks.
Place them in a large Ziploc bag and pour the marinade over them. Seal the bag, removing as much air as possible, and refrigerate for at least 30 minutes. (Obviously, the longer you let the chicken marinate the more it will soak up the glorious flavors, but 30 minutes will do in a pinch.)
Slice your peaches into 16ths. Just to break it down: Cut each peach in half (removing the pit, duh). Then slice each half into four segments. Slice each of those four segments in half. Voila!
Once the chicken is marinated, it’s time to assemble the skewers. Thread a piece of chicken, followed by a basil leaf, and a peach segment onto a soaked bamboo skewer. (Fold large basil leaves in half before threading them onto the skewers.) Repeat this pattern about 3 times per skewer. (You should be able to get 4 pieces of chicken, 3 peaches, and 3 leaves of basil on each skewer, but you can do less if you prefer, okay?)
Heat a clean, oiled grill or grill pan over medium heat. When hot add the skewers and cook, rotating occasionally until the chicken is cooked through, about 12-15 minutes. Serve immediately with extra Sriracha.