In a large Dutch oven or heavy pot, heat oil over medium-high. Season chicken with salt and pepper and cook until it releases its juices and is almost cooked through, about 7 minutes. Add onion and cook until translucent, stirring occasionally, about 6 minutes. Add garlic and cook until fragrant, about 30 seconds. Add cream and bring to a boil. Reduce heat to a rapid simmer and cook, stirring occasionally, until sauce is thick enough to coat the back of a spoon, about 15 minutes. Season to taste with salt and pepper.
Meanwhile, in a large pot of boiling salted water, cook pasta until al dente. Reserve 1 cup pasta water; drain pasta and add to sauce, tossing to combine and adding enough pasta water to create a creamy sauce that coats pasta. Serve immediately.