  We observe the quantum Zeno effect -- where the act of measurement slows the
rate of quantum state transitions -- in a superconducting qubit using linear
circuit quantum electrodynamics readout and a near-quantum-limited following
amplifier. Under simultaneous strong measurement and qubit drive, the qubit
undergoes a series of quantum jumps between states. These jumps are visible in
the experimental measurement record and are analyzed using maximum likelihood
estimation to determine qubit transition rates. The observed rates agree with
both analytical predictions and numerical simulations. The analysis methods are
suitable for processing general noisy random telegraph signals.
