Preheat a grill or grill pan to medium-high.
In a small bowl, mix buttermilk, EVOO, thyme, lemon zest and juice; season with salt and pepper. In a medium bowl, toss the chicken with half of the buttermilk mixture.
Thread chicken onto 8 skewers. Grill, turning frequently, until cooked through and browned in spots, 13 to 15 minutes.
In a large bowl, toss together the romaine, cucumber, onion and grapes. Drizzle with the remaining buttermilk mixture; season. Serve the salad with the kebabs.