Heat oil in a large nonstick skillet over medium-high heat. Place plastic wrap over chicken; pound each piece to a 1/4-inch thickness using a meat mallet or rolling pin. Sprinkle both sides of chicken with fajita seasoning. Add chicken to pan; cook 2 minutes on each side or until done. Cut into (1-inch-thick) slices.
While chicken cooks, combine mayonnaise, cilantro, rind, and juice; spread evenly over cut sides of bread. Arrange chicken on bottom half of bread; top with tomato and arugula. Cover with top half of bread. Cut into 4 wedges.