In a medium mixing bowl, combine 2 tablespoons vegetable oil, lime juice, Worcestershire, brown sugar, minced garlic, jalapeño, chili powder, cumin, 1 teaspoon salt, and 1/2 teaspoon black pepper.
Remove and reserve 1/4 cup of marinade to finish the fajitas later.
To the remaining marinade, add 3/4 teaspoon salt. Add chicken strips to the bowl, cover with plastic wrap, and refrigerate for 20 minutes.
Remove chicken strips from marinade and shake off excess marinade. Heat 2 tablespoons oil in 12-inch nonstick skillet or cast iron pan, over medium-high heat until just smoking.
Add chicken to the hot skillet and brown strips for about, 3-4 minutes, turn and continue to cook until cooked through. The chicken strips are considered done when they reach an internal temperature of 165°F (75°C). Transfer to a plate and tent loosely with aluminum foil.
To the same skillet add 2 tablespoons of oil and heat over medium heat. Add red and green bell pepper, onion, and 1/4 teaspoon salt. Cover and cook, stirring occasionally, until vegetables are soft and beginning to brown, 6 to 8 minutes.
Turn the heat to low, return cooked chicken, add remaining reserved marinade, and toss to combine. Cover and heat until chicken is reheated. Add cilantro, toss and transfer to platter. Serve with warm tortillas.