Preheat a skillet over medium-high heat. Once the skillet is hot, add oil and swirl to coat the bottom. Add chicken strips and cook, turning occasionally, 6-8 minutes, until internal product temperature reaches 165°F on a meat thermometer. Remove from heat.
Meanwhile, wash and dry the fresh produce.
Place vinegar, oil, salt, and pepper in a medium bowl. Whisk to combine the dressing.
Trim, seed, and cut bell pepper into thin matchsticks. Trim and thinly slice cucumbers. Trim and cut green onions crosswise into thin pieces. Set a small handful of green onions aside for serving, then add remaining veggies to the bowl with the dressing. Add shredded carrots and stir to combine the filling.
To serve, separate lettuce into leaves and divide between plates, piling smaller leaves together as needed. Divide chicken and veggie filling between lettuce wraps, then garnish with reserved green onions and chow mein noodles. Enjoy!