Start by generously seasoning your boneless, skinless chicken breasts on both sides with salt, freshly ground black pepper, and dried thyme.
In a medium saucepan, combine the halved cherries, balsamic vinegar, honey, and minced garlic. Cook this mixture over medium heat while stirring occasionally for about 8-10 minutes until it reduces to a glossy glaze.
Heat a grill pan or heavy skillet over medium-high heat.
Add the seasoned chicken breasts to the hot pan and cook for about 6-7 minutes on one side, then flip and cook for another 6-7 minutes or until they reach an internal temperature of 165°F.
Brush the cherry balsamic glaze onto each piece of chicken during the last 2-3 minutes of cooking.
Remove the chicken from heat and let it rest for about 3 minutes.
Serve the cherry balsamic glazed chicken immediately, drizzling any remaining glaze over the top and garnishing with freshly chopped flat-leaf parsley.