Family Farm Antitrust Act of 1979 - Finds that: (1) vertical integration of the agricultural industry by corporations engaged in the processing, distributing, and retail industries, and other conglomerate corporations, tends to create monopolies in the agricultural industry and produce unfair competition for family farms, contributing to the demise of rural communities; (2) the potential for foreign investment in productive agricultural land remains an imminent threat to the family farm; and (3) there is a serious lack of information available on corporate investments in farmland. Amends the Clayton Act to prohibit any person engaged in commerce in a business other than farming, whose nonfarming business assets exceed $15,000,000, from controlling or attempting to control, directly or indirectly, the production of raw farm products through the ownership or long-term leasing of agricultural land. Specifies exceptions to such prohibition including family farms as defined in this Act, farmer owned or controlled cooperatives, and acquisitions of land for research, experimental, and agricultural and resource development purposes. Prohibits any foreign person, as defined in the Agricultural Foreign Investment Disclosure Act of 1978, from acquiring agricultural land unless such land is put to a nonfarming use within five years from its acquisition and is leased during such interim period to a family farm. Requires any entity, the nonfarming business assets of which exceed $15,000,000 and which holds an equity interest in agricultural land to file an annual statement with the Secretary of Commerce on its agricultural activities, the number of acres involved, and the names and addresses of major shareholders in such entity. Prescribes a civil penalty for violations of this Act.