Preheat a grill or grill pan to medium high. Combine 1/4 cup buttermilk, the hot sauce, 1/2 teaspoon salt, and pepper to taste in a large bowl. Add the chicken and turn to coat; let stand 10 minutes.
Meanwhile, make the ranch sauce: Mince the garlic with 1/4 teaspoon salt on a cutting board; mash with the flat side of a chef's knife to make a paste. Combine the garlic paste, mayonnaise, vinegar, the remaining 2 tablespoons buttermilk and the chives in a small bowl. Season with salt and pepper.
Transfer the chicken to the grill, letting the excess marinade drip off. Grill until marked on the bottom, 3 to 4 minutes, then flip the chicken, top each piece with a slice of cheese and continue grilling until just cooked through, 2 to 4 more minutes.
Spread each roll with some of the ranch sauce and fill with the chicken, lettuce and tomato. Serve with potato chips.