In a wide mixing bowl, whisk together the vegetable oil, honey, yellow mustard, and curry powder until smooth.
Remove 1/2 cup of the honey mustard mixture and set aside for brushing while grilling.
Add the chicken pieces to the bowl with the remaining marinade and fold to coat evenly.
Cover and refrigerate the coated chicken for 2 to 4 hours, turning or folding the chicken once halfway through the marinating time.
About 30 minutes before grilling, thread the marinated chicken, red pepper pieces, and onion layers onto skewers, alternating ingredients.
Season the assembled kabobs on all sides with kosher salt and freshly ground black pepper to taste.
Preheat the grill to medium–medium-high and clean and oil the grates.
Grill the kabobs 10–15 minutes total, turning every few minutes so they cook evenly and do not burn; move to a cooler part of the grill or reduce heat if they begin to char.
During the final few minutes of grilling, liberally brush the kabobs with the reserved 1/2 cup honey mustard mixture and grill until the chicken is cooked through.