We present results from three observations with the Rossi X-ray Timing Explorer ( RXTE ) of LMC X-3 , obtained while the source was in an extended ’ low/hard ’ state . The data reveal a hard X-ray spectrum which is well fit by a pure power law with photon index \Gamma =1.69 \pm 0.02 , with a source luminosity at 50 kpc of 5–16 \times 10 ^ { 36 } erg s ^ { -1 } ( 2–10 keV ) . Strong broad-band ( 0.01-100 Hz ) time variability is also observed , with fractional rms amplitude 40 \pm 4 % , plus a quasi-periodic oscillation ( QPO ) peak at 0.46 \pm 0.02 Hz with rms amplitude \sim 14 % . This is the first reported observation in which the full canonical low/hard state behavior ( pure hard power law spectrum combined with strong broad-band noise and QPO ) for LMC X–3 is seen . We reanalyze several archival RXTE observations of LMC X-3 and derive consistent spectral and timing parameters , and determine the overall luminosity variation between high/soft and low/hard states . The timing and spectral properties of LMC X-3 during the recurrent low/hard states are quantitatively similar to that typically seen in the Galactic black hole candidates .