Mix together all marinade ingredients, then divide evenly between two plastic bags or bowls.
Place the chicken in one bag, and the sliced peppers and onions in the other. Transfer to the refrigerator and marinate for at least 2 hours, and up to 24. I find the sweet spot is 6-8 hours.
To cook the chicken and fajita vegetables, the best option is an outdoor grill, the second best is an indoor grill, and the next best is a cast-iron skillet on the stove.
OUTDOOR GRILL: I like using a charcoal grill when cooking outside, and usually cook the chicken for about 10 minutes to get it at an internal temperature of 165F (time will vary depending on heat of grill and size of the chicken breasts). To keep the peppers and onions from falling through, you will likely need to put them in a wire basket. I find they are crisp-tender when cooked for about 12-15 minutes.
INDOOR GRILL: The nice thing about an indoor grill is it gives the food a nice char and flavor, however you don't get the hot heat through the surrounding air like you do with a real grill, so you may need to supplement with other types of heat. I sear the chicken until caramelized on both sides, about 4-5 minutes on each side, but if the chicken starts to get too dark and isn't cooked through, put the chicken into the oven to get it to 165F. With the vegetables, I often will start it on the indoor grill to char, then soften it further in a skillet on the stove. After grilling, it usually only needs about 5 minutes in the skillet.
CAST-IRON SKILLET ON STOVE: Sear the chicken over medium high heat for about 5 minutes on each side, until caramelized and cook through to 165F. If the chicken gets too dark on the outsides before cooking through to the middle, you may finish cooking in the oven. Cook the peppers and onions in the skillet, about 10 minutes total, over medium high heat, until crisp-tender and slightly softened.
Let the chicken rest for at least 10 minutes after cooking, then slice and serve with the peppers, onions, and accompaniments.
My favorite way to eat the fajitas is to tear off small pieces of flour tortilla, and wrap up the chicken, vegetables, and ingredients to be enjoyed in small bites. Enjoy!