Heat 1 tablespoon oil in a large skillet over medium-high heat until hot.
Add chicken strips and cook, stirring a couple of times, until almost cooked through, 5 to 6 minutes.
Add half of fajita seasoning and water, mix well, and let chicken finish cooking.
Transfer chicken to a bowl; cover to keep warm.

Heat remaining 1 tablespoon oil in skillet until hot.
Add onions and peppers; cook, without stirring, until tender and some caramelized brown bits begin to show up in pan, 3 to 4 minutes.
Stir; add garlic and remaining fajita seasoning. Let cook about 2 more minutes.
Stir vegetables into seasoned chicken. (Or serve the vegetables separately.)

Serve the fajita mixture on warm tortillas with salsa and sour cream on the side, if using.