We have identified a new transient luminous low-mass X-ray binary, NGC 6440 X-2, with Chandra/ACIS, RXTE/PCA, and Swift/XRT observations of the globular cluster NGC 6440. The discovery outburst (July 28-31, 2009) peaked at L_X~1.5*10^36 ergs/s, and lasted for <4 days above L_X=10^35 ergs/s. Four other outbursts (May 29-June 4, Aug. 29-Sept. 1, Oct. 1-3, and Oct. 28-31 2009) have been observed with RXTE/PCA (identifying millisecond pulsations, Altamirano et al. 2009a) and Swift/XRT (confirming a positional association with NGC 6440 X-2), with similar peak luminosities and decay times. Optical and infrared imaging did not detect a clear counterpart, with best limits of V>21, B>22 in quiescence from archival HST imaging, g'>22 during the August outburst from Gemini-South GMOS imaging, and J>~18.5$ and K>~17 during the July outburst from CTIO 4-m ISPI imaging. Archival Chandra X-ray images of the core do not detect the quiescent counterpart, and place a bolometric luminosity limit of L_{NS}< 6*10^31 ergs/s (one of the lowest measured) for a hydrogen atmosphere neutron star. A short Chandra observation 10 days into quiescence found two photons at NGC 6440 X-2's position, suggesting enhanced quiescent emission at L_X~6*10^31 ergs/s . NGC 6440 X-2 currently shows the shortest recurrence time (~31 days) of any known X-ray transient, although regular outbursts were not visible in the bulge scans before early 2009. Fast, low-luminosity transients like NGC 6440 X-2 may be easily missed by current X-ray monitoring.
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