We report on our experimental implementation of QKD with orthogonal states. Since, in general, non-orthogonal states cannot be cloned, any eavesdropping attempt in a Quantum Communication scheme using non-orthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in Quantum Cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets travelling along separate channels. Here we describe in detail the first experimental realization of a quantum cryptography system based on orthogonal states and the measures of the main parameters that quantify the quality of the system. Our results demonstrate the possibility of achieving a QKD transmission based on orthogonal state with a Quantum Bit Error Rate comparable with more common secure QKD systems. Therefore, it provides a significant hint to the discussion on the minimal quantum resources necessary for the implementation of quantum tasks overcoming classical limits.