In a small bowl, combine 1/2 cup water with the fish sauce, soy sauce, sugar and crushed red pepper. Stir to dissolve the sugar; set aside.
In a large pot of boiling, salted water, cook the rice noodles until al dente. Drain and set aside.
While the noodles are cooking, heat a wok or large, deep skillet over medium-high heat until hot, about 1 minute. Add 2 tablespoons oil, then the sliced and chopped onion, and garlic. Stir-fry until fragrant and softened but not browned, about 3 minutes. Transfer the mixture to a bowl and set aside.
Add the remaining 1 tablespoon oil to the skillet and heat for about 1 minute. Working in 2 batches if necessary, spread the chicken in a single layer in the pan without crowding and cook, undisturbed, until the edges change color, about 1 minute. Turn and continue cooking, tossing now and then, until lightly browned all over, 2 to 3 minutes. Add the reserved sauce and onion mixture and cook, tossing occasionally, until the chicken is cooked through and evenly coated, 2 to 3 minutes longer. Remove the pan from the heat and add the basil, tossing until slightly wilted. Serve the chicken over the noodles.