Add the olive oil, Dijon mustard, honey, apple cider vinegar or lemon juice, garlic, salt, smoked paprika, thyme, and black pepper to a large bowl. Whisk until well combined.
Reserve a few tablespoons of the honey mustard marinade for serving. Add the chicken breasts to the remaining marinade and turn them until they're completely coated. Cover and refrigerate for at least 2 hours.
Preheat the grill to medium-high heat, about 400°F. Clean the grill grates and lightly oil them to help prevent the chicken from sticking.
Remove the chicken from the marinade. Discard any marinade that has been in contact with the raw chicken.
Place the chicken breasts directly on the hot grill. Grill for about 5-7 minutes on the first side without moving them. This gives the chicken time to develop good grill marks and release naturally from the grates.
Flip the chicken and continue grilling for another 5-7 minutes, or until cooked through. Very thick chicken breasts may take a few minutes longer.
Check the thickest part of each chicken breast with an instant-read meat thermometer. Cook until the chicken reaches 160°F.
Transfer the chicken to a clean plate or cutting board and let it rest for 5 minutes before slicing. Drizzle with the reserved honey mustard sauce and serve.
Notes
I recommend going by temperature rather than cooking time since chicken breasts can vary quite a bit in size.