Heat corn oil in a skillet over medium heat. Cook and stir chicken and garlic until chicken is no longer pink in the center and juices run clear, 4 to 6 minutes.
Transfer chicken to a plate.
Pour wine in the same skillet and simmer, about 2 minutes.
Stir cream into simmering wine; reduce heat and simmer until large bubbles appear, 2 to 4 minutes.
Cook and stir chicken, tomatoes, salt, and black pepper into cream mixture until all ingredients are warmed, 2 minutes.
Bring a large pot of lightly salted water to a boil. Stir in pasta and asparagus; cook until pasta floats to the top, about 3 minutes.
Drain.
Toss pasta and asparagus together with chicken and cream sauce. Top with Parmesan cheese.
