We propose a method to perform single-shot optical readout of a quantum bit (qubit) using cavity quantum electrodynamics. We selectively couple the optical transitions associated with different qubit basis states to the cavity and utilize the change in cavity transmissivity to generate a qubit readout signal composed of many photons. We show that this approach enables single-shot optical readout even when the qubit does not have a good cycling transition, which is required for standard resonance fluorescence measurements. We calculate the probability that the measurement detects the correct qubit state using the example of a quantum-dot spin under various experimental conditions and demonstrate that it can exceed 0.99.