We experimentally demonstrate a complete, end-to-end, quantum key distribution system using a continuous wave laser and standard optical components. Our implementation encodes random bits as weak Gaussian modulations onto the phase and amplitude quadratures of the laser beam. We process data from the quantum channel using a post-selection procedure and subsequently apply information reconciliation and privacy amplification procedures to generate an absolutely secure secret key. The maximum information that an eavesdropper may have obtained about this secret key, from the quantum channel and classical communications, is bounded to below one bit. Under the assumption of individual Gaussian eavesdropping attacks, we achieve a secret key generation rate of 25 Mbits/s for a lossless channel and 1 kbit/s for 90% channel loss, per 17 MHz of detected bandwidth.