Heat the oil in the wok and stir-fry the onions, carrots, and snow peas for 2 minutes. Add the lemon basil and chicken and stir-fry for 2 more minutes.
Add the garlic, soy sauce, rice vinegar, palm sugar, toasted sesame oil, and black pepper and stir-fry for 30 seconds.
Serve immediately straight out of the wok if you want to be casual, or on a bed of the shredded romaine for presentation.