Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Place chicken and chorizo in a large bowl. Add olive oil, sherry vinegar, oregano, cayenne pepper, salt, and black pepper; stir until chicken and chorizo are completely coated.

Thread chicken, chorizo, red onion, and bell pepper evenly onto 4 skewers, making sure that each piece chicken touches 1 piece chorizo. Place threaded skewers on a plate, cover with plastic wrap, and refrigerate until cold, 15 to 30 minutes.

Cook on the preheated grill, turning occasionally, until chicken is cooked through, about 10 minutes.