We demonstrate the initialisation, read-out and high-speed manipulation of a qubit stored in a single 87 Rb atom trapped in a submicron-size optical tweezer. Single qubit rotations are performed on a sub-100 ns time scale using two-photon Raman transitions. Using the "spin-echo" technique, we measure an irreversible dephasing time of 34 ms. The read-out of the single atom qubit is at the quantum projection noise limit when averaging up to 1000 individual events.