Is monogamy natural for humans?

In Brave New World, Aldous Huxley described a progressive utopia in which everyone is happy because everyone is engineered to fit the environment. One feature of that environment is the doctrine that "Everyone belongs to every one else." Promiscuity is required as the norm, since families and parents are seen as causes of strife. In the interest of stability in society, the babies are made by the state and conditioned for their future roles. Free love is the norm to prevent individual attachments (like mother and son or husband and wife) which lead to jealousy and possessiveness and strife and struggle.

Would humans thrive in such freedom? Or would they crave more permanent relationships, which must perforce exclude others?