Heat olive oil in a large skillet over medium heat.
Season chicken breasts with salt and pepper, then add to the skillet. Cook until browned on both sides, about 5-7 minutes per side. Remove chicken and set aside.
In the same skillet, add onions and garlic. Cook until softened, about 3 minutes.
Add mushrooms and cook until they release their moisture and start to brown, about 5 minutes.
Pour in chicken broth and bring to a simmer. Add heavy cream and stir to combine.
Return chicken to the skillet, cover, and simmer until chicken is cooked through, about 10-15 minutes.