Bring a medium pot of water to a boil. Add noodles and cook until softened, about 4 minutes. Drain and rinse with cold water. Set aside.
Heat oil in a wok or large frying pan over high heat. Add garlic and shallots and cook until fragrant, about 30 seconds. Add chicken, curry paste, and half the coconut milk. Stir well to dissolve paste and boil until liquid is slightly reduced, about 5 minutes. Stir in remaining coconut milk, the sugar, lime juice, soy sauce, and fish sauce, then bring to a boil. Reduce heat and simmer until liquid is slightly thicker, 2 to 3 minutes more.
Add noodles, toss to coat, and cook a few minutes until hot, stirring often. Pour mixture into a serving bowl. Sprinkle with green onions, cilantro, and basil. Serve with lime wedges.
*Find in grocery stores' Asian foods aisle, at Asian markets, or on amazon.com. Use regular basil if Thai isn't available.