Combine pesto and mayonnaise in a small bowl, stirring to blend.
Sprinkle chicken with pepper and salt. Heat oil in a large nonstick skillet over medium-high heat. Add chicken, and cook for 3 minutes on each side or until done. Remove chicken to cutting board, and cool slightly. Cut chicken lengthwise into thin slices.
Cut ciabatta in half horizontally. Place bread, cut sides up, on a baking sheet. Broil 3 minutes or until lightly browned. Remove bread from pan. Spread pesto mixture evenly over cut sides of bread. Arrange the chicken slices evenly over bottom half. Top chicken evenly with basil leaves, and sprinkle cheese over top. Place bottom half on baking sheet, and broil 2 minutes or until cheese melts. Arrange bell pepper and tomato over cheese, and cover with top half of bread. Cut into 4 equal pieces.