Bring 2 quarts of water to a boil in a stockpot. Add asparagus; cook 3 minutes. Remove with a slotted spoon. Add pasta to boiling water; cook according to package directions, omitting salt and fat. Drain.
Cut the chicken crosswise into 1/4-inch-wide-strips. Heat oil in a large nonstick skillet over medium-high heat. Add chicken; sauté 5 minutes. Add asparagus, peas, salt, pepper, and garlic; sauté 2 minutes. Stir in wine, scraping pan to loosen browned bits. Stir in cream and juice; cook 1 minute. Add pasta and cheese; stir well to coat. Remove from heat; stir in basil, green onions and parsley.