Mix olive oil, balsamic vinegar, garlic, salt & pepper. Cut each chicken breast in half and marinade in the balsamic mixture for 1 hour.
Mix all ingredients for the garlic aioli and refrigerate until ready to use.
Grill chicken breasts until cooked.
Butter ciabatta buns, and toast them on BBQ grill or hot pan (30 seconds - 1 minute).
Spread garlic aioli on the bottom ciabatta bun. Place brie cheese on top, then chicken breast, then arugula. Drizzle Balsamic Reduction over the arugula, and place the other half of the ciabatta bun on top.
Serve immediately.