Heat olive oil in a heavy skillet over medium-high heat and cook onions until soft and translucent, about 5 minutes. Add chicken and carrots and cook until chicken is browned on all sides and carrots are tender, 5 to 10 minutes.
Pour in champagne and simmer until alcohol has evaporated, 3 to 5 minutes. Add cream and chicken base and simmer until sauce has thickened, 10 to 15 minutes.
