Mix first three ingredients in a small bowl. Mix in chopped arugula. Season arugula mayonaise generously with ground pepper. (Can be made 1 day ahead. Cover and chill) Char peppers over gas flame or in broiler until blackened on all sides. Place in bag and let stand 10min. Peel and seed peppers. Cut into 1/2" wide strips. Sprinkle chicken with salt and pepper. Heat large non stick skillet over medium-high heat. Brush skillet with 1t oil. Add chicken, saute until just cooked through about 4 min per side. Transfer to plate; cool and cut into diagonal slices.

Spread generously 2t arugula mayo on each side of the bread. Cover bottom of bread pieces generously with arugula. Top with sliced chicken dividing equally. Top with bell pepper strips and generous amount of arugula. Cover with bread tops.