In a small bowl, add the olive oil, 1 teaspoon kosher salt, and 1 teaspoon smoked paprika. Stir until well mixed.
Rub the oil mixture evenly over the chicken.
Set the chicken aside.
In a blender, add the cherries, apple cider vinegar, molasses, Dijon mustard, remaining ¼ teaspoon smoked paprika, and remaining ¼ teaspoon kosher salt. Blend until smooth. Set the smoky cherry sauce aside.
Preheat a gas or charcoal grill to medium-high heat.
Place the chicken on the grill. Grill the chicken for 2 to 3 minutes.
Flip the chicken. Grill for another 2 to 3 minutes, or until cooked through.
Place the chicken on a serving plate. Let the chicken rest for 5 minutes.
Slice the chicken. Slice the chicken. Sprinkle chopped chives over the top.
Store in Refrigerator - Place leftover chicken and sauce in an airtight container. Refrigerate for up to 3 days.Store Sauce Separately - Keep the smoky cherry sauce in a separate container when possible. This helps the chicken hold its texture.Reheat on Stovetop - Place the chicken in a skillet over low heat with 1 to 2 tablespoons water. Warm until heated through.Reheat in Microwave - Place one serving on a microwave-safe plate. Cover loosely and heat in short intervals until warm.