In a small bowl, combine mayonnaise, cilantro and lime juice and stir to combine.
In a large bowl, combine chicken, beans and mango and stir.
To assemble burritos, spread each tortilla with a heaping tablespoon of mayonnaise mixture, leaving a ¼-inch border around the edge. Place about 1/3 cup chicken mixture in the center of each tortilla. Tuck in the sides and then wrap and roll the tortillas.