Current security systems typically rely on the adversary's computational limitations (e.g., the fact that it cannot invert a hash function or perform large-integer factorization). Wireless networks offer the opportunity for a different, complementary kind of security, which relies not on the adversary's computational limitations, but on its limited network presence (i.e., that the adversary cannot be located at many different points in the network at the same time). We take a first step toward designing and building a wireless security system that leverages this opportunity: We consider the problem where a group of n nodes, connected to the same broadcast wireless network, want to agree on a shared secret (e.g., an encryption key), in the presence of an adversary Eve who tries to listen in and steal the secret. We propose a secret-agreement protocol, where the n nodes of the group keep exchanging bits until they have all agreed on a bit sequence that Eve cannot reconstruct (with very high probability). We provide experimental evidence -- to the best of our knowledge, the first one -- that a group of wireless nodes can generate thousands of new shared secret bits per second, with their secrecy being independent of the adversary's computational capabilities.