Heat olive oil in a pot over medium heat. Add the peppers and onion and cook down about 6-7 minutes, until softened. Add peaches and cook another 2-3 minutes to soften. Add vinegar, water, jerk seasoning, and brown sugar. Reduce heat and simmer for about 10 minutes to allow flavors to develop, while stirring. Once completed, finish with butter and set aside.
In a large bowl, combine jalapeños, red onion, peaches, cilantro, lime juice, and season to taste. Cook chicken according to package directions and toss with the peach jerk sauce. Garnish with the peach salsa, grilled peaches and enjoy!