Human-Animal Hybrid Prohibition Act of 2007 - Amends the federal criminal code to prohibit and to set penalties for: (1) creating or attempting to create a human-animal hybrid (a being with human and non-human tissue as specified in this Act); (2) transferring or attempting to transfer a human embryo into a non-human womb, or a non-human embryo into a human womb; or (3) transporting or receiving for any purpose a human-animal hybrid.