Slice the chicken into thin strips, then add to a plastic zip-top bag along with the garlic, balsamic vinegar, honey, salt, pepper, and olive oil. Seal the bag, then use your hands to squish the chicken around to mix together and fully coat with all the ingredients. Refrigerate for at least 4 hours or overnight.
Make the honey balsamic butter by combining balsamic vinegar, honey, and garlic in a medium saucepan over medium heat. Season with salt and pepper, then bring up to a rapid simmer. Al-low the liquid to reduce by a little less than half – it should become thick and syrupy. Turn off the heat then whisk in the butter until smooth. Set aside.
Preheat a grill to medium-high heat. Skewer the chicken pieces by weaving them over and un-der, like an accordion, making sure they are nice and compact. Grill until charred on one side, about 3-4 minutes. Flip, then brush the cooked side generously with honey balsamic butter.
Remove from the grill once charred on the other side and cooked through in the center. Brush with more honey balsamic butter to coat on all sides before serving.