In a plastic bag, combine chicken tenders and 1/4 cup of pesto, set aside and let sit for 15 minutes.
In a small bowl, stir together 1/4 cup pesto and mayonnaise. Spread mixture on both sides of ciabatta; set aside.
Preheat an oiled grill pan over medium-high heat. Grill chicken tenders 5 minutes per side. Remove and let rest for 5 minutes. Turn the heat down to medium and re-oil the grill pan.
Place cheese on both halves of bread. Add arugula, then tomato, then basil leaves, then pesto chicken to bottom piece. Top with top half of bread. Place onto the grill pan and place a heavy pan on top of the sandwich. Grill for 3 minutes per side or until cheese starts to melt.