In a medium bowl, mash 2 cups of blackberries well. Combine with olive oil, balsamic vinegar, hot sauce, white sugar, and steak seasoning. Add chicken breasts to a large zip-lock bag, pour in the marinade, seal and shake to coat evenly.

Refrigerate for at least 4 hours or up to 24 hours. Turn the bag every couple of hours for even marinating. The chicken will turn a deep purple color from the berries. This is normal.

Heat your grill to medium heat. If chicken breasts are very thick, pound them to an even thickness with a meat mallet for more even cooking.

In a small saucepan, whisk cornstarch into cold water before turning on heat. Add sugar, balsamic vinegar, and blackberries. Cook over medium heat, mashing the berries and stirring until the glaze thickens, about 4 minutes. Reduce to low and keep warm.

Grill chicken for 5 to 8 minutes per side, flipping once, until the internal temperature reaches 165 degrees F on a meat thermometer. Do not press down on the chicken while grilling.

Plate the hot grilled chicken and spoon the warm blackberry balsamic glaze generously over the top. Serve immediately.