Whisk the sauce together in a small bowl. Place the sliced chicken in another bowl and spoon 3 tablespoons of sauce over the top to marinade. Mix and set aside.
Chop the rest of the ingredients. Boil a large pot of water and cook the noodles according to the package instructions.
Meanwhile heat the wok (or a large skillet) to high heat. Add a teaspoon of oil to the skillet and quickly scramble the eggs. Push the eggs up the side of the wok and add the chopped onions, thai chiles, and garlic. Stir fry for 2 minutes, then add the chicken, and another teaspoon of oil if needed. Stir fry until just barely cooked through (3-5 minutes) and push the mixture up the side of the wok. *If using a skillet, transfer the cooked items to a separate dish and add back to the skillet after the noodles, or they will over-cook.
Now add the bell peppers and carrots. Stir fry for 2 minutes, then mix all the ingredients and pour the drained noodles over the top. Add the remaining sauce, thai basil, tomatoes, and green onions. Toss and stir fry another minute. Then remove from heat and serve warm with lime wedges.
Keep Pad Kee Mao leftovers stored in an airtight container in the fridge for up to 3-4 days. It is not recommended that you freeze rice noodle dishes.