Cook fettuccine as directed on package; drain.
Meanwhile, in 12-inch skillet or Dutch oven, heat oil over medium-high heat until hot. Add chicken; cook 4 to 5 minutes, stirring occasionally, until chicken turns white. Stir in garlic and taco seasoning mix. Cook 1 minute. Stir in cream. Reduce heat to low; cook 3 to 5 minutes, stirring constantly, until thoroughly heated.
Stir in 1/3 cup parsley and 1/4 cup cheese. Add cooked fettuccine; toss to coat. Cook 1 minute, stirring constantly, until fettuccine is thoroughly heated. Transfer mixture to large serving platter. Garnish with additional parsley and cheese.