In a glass bowl, whisk together all of the marinade ingredients.
Place the drumsticks in a ziplock bag, or a glass or ceramic dish. Do not use a metal dish - the acid in the marinade will react with the metal.
Pour the marinade over the chicken. Turn the chicken to coat it. If you're using a ziplock bag, seal the bag and "massage" the chicken to coat it thoroughly.
Marinate the chicken in the refrigerator for at least 4 hours and up to 24 hours.
The chicken
Remove the chicken from the refrigerator 15 to 20 minutes before cooking. This will help the chicken cook more evenly on the grill.
Heat the grill to medium-high heat (about 400 degrees F). Once the grill is hot, brush the grates with oil to prevent sticking. A use an oil with a high smoke point, such as avocado oil.
Place the chicken on the grill and close the lid. Cook the chicken, turning every 5 minutes, until the internal temperature reaches 165 degrees F, about 25 to 35 minutes, depending on the thickness of the meat. If the chicken is sticking to the grill the first time you try to turn it, let it cook for several additional minutes before trying to turn it again. This will allow a crust to form and the chicken should release easily from the grill.
The glaze
In a small saucepan, whisk together the balsamic vinegar and maple syrup. Bring to a boil over medium-high heat, whisking very frequently. Reduce the heat so the glaze is simmering. Cook, whisking frequently, until the glaze becomes thicker, about 5 minutes.
Once the chicken is cooked, brush the chicken with the glaze. Cook for 1 minute, brush the other side with the glaze and cook for 1 minute. Let the chicken rest for a few minutes. Serve.
Video
Notes
Note: I used Morton kosher salt. If using Diamond Crystal kosher salt, you may need to use additional salt. I suggest 2 ¼ to 2 ½ teaspoons of Diamond Crystal salt for the marinade.Please note that I am not a medical or nutritional professional. I provide nutritional information for my recipes as a courtesy to my readers. It is calculated using the built-Lose It! calculator. While I attempt to provide information that is as accurate as possible, you should calculate the nutritional information independently before relying on it.More on nutritional calculation: I calculated the numbers using one-third of the marinade ingredients, estimating the amount of marinade that would absorb into or stick to the chicken.