Place peach in a food processor or blender and blend on high until smooth.
Combine peach puree, honey, sugar, vinegar, mustard, garlic, and rosemary sprigs in a medium saucepan and season with salt and pepper to taste.
Bring glaze to a simmer over medium-high heat, then reduce heat to low and allow to simmer 10-15 minutes, stirring occasionally, until glaze is reduced and sticky in consistency. Remove rosemary sprigs and discard. Set aside half of glaze for serving with chicken later.
Preheat a grill to 400F OR heat a large skillet over medium-high heat if cooking indoors and oil well. Season chicken all over with salt and pepper to taste.
Place chicken on preheated grill or in pan in a single layer. Cook chicken 8-10 minutes at 400F, brushing well with glaze and turning frequently throughout cooking until chicken registers 165F.
Remove chicken from grill and serve warm with reserved glaze brushed on top. Enjoy!