Place the chicken, margarita mix, tequila, cilantro and chicken seasoning in a large resealable plastic bag; squeeze out the air and seal. Massage the bag to combine the ingredients. Refrigerate for 30 minutes to 1 hour. Meanwhile, soak 12 wooden skewers in water.
Preheat a grill to medium. Remove the chicken from the marinade; thread each piece onto a skewer. Oil the grill grate; grill the chicken skewers for 1 to 2 minutes per side, or until the meat is cooked through. Serve on a platter with arugula and lime.