In a small bowl, stir together oil, 1 tsp salt and 1 tsp paprika; rub evenly over chicken and set aside.
Into a blender place cherries, vinegar, molasses, mustard and remaining 1/4 tsp each smoked paprika and salt; blend until smooth and set aside.
Make sure your grill grates are super clean. Preheat a gas or charcoal grill to medium-high heat (or set a large grill pan over two burners or broil).
Grill chicken, flipping once, until cooked through, 2-3 minutes per side. Let chicken rest for 5 minutes before slicing; serve drizzled with sauce and sprinkled with chives.
Serving size: 3 oz chicken, 3 Tbsp sauce