Prepare a grill for medium high heat cooking.
Toss the tomatoes with 1 tablespoon olive oil and season with salt. Arrange the tomatoes cut side up on a foil lined baking sheet and set on the grill. Cook the tomatoes until the skin is charred and they are soft and juicy, about 10 minutes.
While the tomatoes cook, butterfly the chicken breast. Remove the chicken breast from the fridge and pat dry with paper towels. Use a sharp knife to butterfly the breast — place your hand on the breast and slice through it starting at the thickest part to slice it in half horizontally. Cover the breast with plastic wrap or use a zip top bag and use a mallet to pound the thickest sections to about ¼ inch thickness. Season the pieces on all sides with salt and pepper and the remaining tablespoon of olive oil.
Grill the chicken over direct heat. After two minutes, rotate the chicken 45 degrees. After two more minutes flip and repeat. Remove the chicken from the grill, it should reach 165 ºF. Halve each half to give you 4 pieces.
Build the sandwiches by toasting the ciabatta buns for 1-2 minutes. Spread each bun half with a spoonful of pesto, then top with a piece of grilled chicken, mozzarella slices, blistered tomatoes, arugula, red onion and a top bun for closure.