The globular cluster NGC 6440 is known to harbor a bright neutron-star X-ray transient. We observed the globular cluster with Chandra on two occasions when the bright transient was in its quiescent state in July 2000 and June 2003 (both observations were made nearly 2 years after the end of their preceding outbursts). The quiescent spectrum during the first observation is well represented by a two component model (a neutron-star atmosphere model plus a power-law component which dominates at

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... gies above 2 keV). During the second observation (which was roughly of equal duration to the first observation) we found that the power-law component could no longer be detected. Our spectral fits indicate that the effective temperature of the neutron-star surface was consistent between the two observations. We conclude that the effect of the change in power-law component caused the 0.5-10 keV flux to be a factor of ~2 lower during the second observation compared to the first observation. We discuss plausible explanations for the variations, including variable residual accretion onto the neutron star magnetosphere or some variation in the interaction of the pulsar wind with the matter still outflowing from the companion star.