The first publicly known key-agreement protocol that meets these criteria was Diffie-Hellman key exchange, in which the two people jointly exponentiate a generator with random numbers, in such a way that an eavesdropper has no way of guessing what the key is.
Diffie-Hellman was first developed by researchers at GCHQ, the UK equivalent to NSA. James Ellis[?] demonstrated that non-secret encryption was possible in the '60s and Malcolm Williamson developed what is now called Diffie-Hellman Key exchange in the early '70s. GCHQ did not allow publication, so Diffie and Hellman were the first to publish.
See the appendix to Crypto[?], by Steven Levy for more information on GCHQ's work, The Code Book[?] by Simon Singh[?], or the GCHQ Web page about 'non-secret encryption'. The latter contains an essay by James Ellis himself.
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