Cook noodles in large pot of boiling salted water until tender but still firm to bite, stirring frequently. Drain.
Meanwhile, heat oil in heavy large pot over medium-high heat. Add garlic and Thai chiles; sauté 30 seconds. Add chicken and next 4 ingredients and sauté until chicken is cooked through, about 4 minutes. Add noodles, tomatoes, and Anaheim chiles; toss to coat. Transfer to large platter, sprinkle with basil leaves, and serve.
*Thai Basil is purple on one side. Available in the Asian foods section or produce section of some supermarkets, and at Southeast Asian and some Asian markets.