In a bowl, combine all spice ingredients setting one tablespoon aside for the peppers and onions.
Spread chicken strips in a single layer on a pie plate or large platter and sprinkle the spice mixture (except the reserved tablespoon) over the top. Using tongs, mix until the chicken is well covered.
Heat a large heavy skillet (cast iron is preferable) over medium-high heat and add the olive oil. Just as it starts to smoke, add 1 tbsp butter, and then turn the heat down to medium.
Cook your chicken in batches (don’t crowd the pan) for 5-8 minutes, turning frequently.
Remove each batch to a plate and continue until all the chicken is cooked, adding more olive oil and butter each time.
In the same hot pan, add more olive oil and sauté peppers and onions.
Sprinkle in the remaining tablespoon of spice mixture and cook, stirring occasionally, for another 4-5 minutes or until vegetables are tender and well coated with spice. Add 1-2 tbsp of lime juice to the hot pan to deglaze.
Remove from heat, move peppers and onions to one side, and add the chicken back to the pan on the other side.
Serve with warm tortillas, your favourite toppings and, if you like, wedges of lime to squeeze over the fajitas.