In a food processor, pulse the anchovies, garlic, parsley, basil, dill and oregano until coarsely chopped. Add the mayonnaise and lemon juice and process until smooth. Fold in the chives; season with salt and pepper.
In a large bowl, toss the ciabatta with the chicken, piquillo peppers, celery and olives. Add the dressing and toss to coat. Season with salt and pepper and serve.