Combine all ingredients for marinade and pour into a plastic ziploc bag. Add chicken, seal, and marinate for at least 30 minutes.
Heat grill on high. Add chicken, grill for 2-3 minutes, turn, and grill for another 2-3 minutes or until chicken registers 160 degrees F on an instant read thermometer. Remove and reserve.
Spread each piece of bread with 1/2 tablespoon of pesto. Slice the tomato into 8 slices. Place chicken on four of the bread slices. Top chicken with Brie slices, arugula, and 2 tomato slices. Top with prepared bread slices, pesto side toward the tomato.
Brush the outside of each sandwich with about 1/2 tablespoon of olive oil. Place on grill, reduce heat to medium, and grill for 2-3 minutes per side or until bread is nicely toasted with grill marks. Cheese should be melted.