The future development of quantum information using superconducting circuits requires Josephson qubits with long coherence times combined to a high-delity readout. Major progress in the control of coherence has recently been achieved using circuit quantum electrodynamics (cQED) architectures, where the qubit is embedded in a coplanar waveguide resonator (CPWR) which both provides a well controlled electromagnetic environment and serves as qubit readout. In particular a new qubit design, the transmon, yields reproducibly long coherence times. However, a high-delity single-shot readout of the transmon, highly desirable for running simple quantum algorithms or measuring quantum correlations in multi-qubit experiments, is still lacking. In this work, we demonstrate a new transmon circuit where the CPWR is turned into a sample-and-hold detector, namely a Josephson Bifurcation Amplifer (JBA), which allows both fast measurement and single-shot discrimination of the qubit states. We report Rabi oscillations with a high visibility of 94% together with dephasing and relaxation times longer than 0.5 $mu$s. By performing two subsequent measurements, we also demonstrate that this new readout does not induce extra qubit relaxation.