Single-shot readout of individual qubits is typically the slowest process among the elementary single- and two-qubit operations required for quantum information processing. Here, we use resonance fluorescence from a single-electron charged quantum dot to read out the spin-qubit state in 800 nanoseconds with a fidelity exceeding 80%. Observation of the spin evolution on longer time scales reveals quantum jumps of the spin state: we use the experimentally determined waiting-time distribution to characterize the quantum jumps.