Mix the diced chicken breast with the marinade ingredients (salt, pepper, smoked paprika, dried oregano, garlic powder (or fresh minced garlic), lemon zest, lemon juice, and olive oil). Cover and set aside to marinate for at least 30 minutes and up to 2 hours.
Assemble the skewers. Start and end with a slice of chorizo as it keeps everything nicely contained. Alternate between chicken and peppers, onions, and chorizo. Use about 4 pieces of chicken, 3 slices of chorizo, 2 pieces of bell pepper, and 2 pieces of onion per wooden skewer when assembling.
Preheat the grill pan over medium-high heat. Cook the skewers, turning them every 2-3 minutes, until the chicken is fully cooked. The chicken is cooked through when it reaches an internal temperature of 165°F (74°C) in the thickest part. Depending on your grill and the size of the chicken pieces, it could take 10-15 minutes. If you have a standard-size grill pan, you will need to cook the chicken skewers in batches (likely 2 batches of 4 skewers).