In a medium bowl, whisk the oil, lime juice, chili powder, cumin, salt, and pepper together.
Place the chicken and vegetables into two separate resealable bags or bowls. Divide the marinade between the two bags. Close to seal and gently massage to evenly coat the chicken and vegetables.
Stash the chicken and vegetables in the fridge and marinate for 1 to 2 hours.
Preheat the Blackstone or griddle to medium-high.
Add the onion, pepper, and marinade from the bag to one side of the griddle. Cook, stirring occasionally, until the vegetables are tender, about 8 minutes.
After the vegetables have been cooking for about 3 minutes, add the chicken and marinade to the other side of the griddle. Cook, stirring frequently, until the chicken is cooked through, 4 to 5 minutes.
Combine everything together on the griddle surface, then scoop into a serving bowl. If desired, warm the tortillas on the hot griddle for 10 to 15 seconds per side.
Serve immediately with your favorite fixings on the side.