Trim the chicken breasts of any fat and cartilage, and cut in 2 inch chunks.
Remove skin from the onion and cut in half. Cut each half into 3 pieces, the long way, and then cut in half through the short way, keeping the layers together as much as possible.
Remove the stem from the pepper, and cut in half, end to end. Pull out any membranes and seeds, and cut each half into 3 long strips, then cut the strips in half the short way. For both the onions and peppers, you want to have pieces about the same size as the chicken.
Place the chicken and peppers in medium sized bowl.
Add the olive oil, salt, pepper, paprika, cumin and garlic and mix gently, but well with a wooden spoon.
Drizzle a bit of oil over the onion chunks, and sprinkle with some salt and pepper - if you put them in the bowl with the chicken and peppers, the layers will not stay together.
String the chicken chunks and vegetable evenly on 4 metal skewers. The chunks of chicken and veggies should be touching, but not pushed together super tightly.
You may have some peppers and onion chunks leftover - I just string those on a separate skewer to serve alongside.
Allow the skewers to sit for about 15 minutes.
Prepare your gas or charcoal grill, making sure to oil the grates, using vegetable oil on a paper towel, held in a pair of long tongs.
Grill the kebabs over medium heat, turning to cook all sides evenly, for about 15 minutes.
Brush all sides of the kababs with a generous amount of Mild to Wild Southwest Chipotle BBQ Sauce, and cook another 5 minutes or so to get a nice glaze on everything.
Serve hot and store any leftover in the refrigerator.