Lightly brown the chicken in a hot pan with the oil. Remove to a side dish. Add mushrooms to the hot pan with the garlic and sauté for 5 minutes, stirring often.
Put the chicken back into the pan and cook for 3-4 minutes more. Add the cream and stir. Reduce the heat to a simmer. Cover the pan and cook slowly until the chicken is cooked trough, about 20 minutes.
Taste for seasoning, and serve, with vegetables or rice.
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