We have discovered a new transient low-mass X-ray binary , NGC 6440 X-2 , with { \it Chandra } /ACIS , { \it RXTE } /PCA , and { \it Swift } /XRT observations of the globular cluster NGC 6440 . The discovery outburst ( July 28-31 , 2009 ) peaked at L _ { X } \sim 1.5 \times 10 ^ { 36 } ergs s ^ { -1 } , and lasted for < 4 days above L _ { X } = 10 ^ { 35 } ergs s ^ { -1 } . Four other outbursts ( May 29-June 4 , Aug. 29-Sept. 1 , Oct. 1-3 , and Oct. 28-31 2009 ) have been observed with { \it RXTE } /PCA ( identifying millisecond pulsations , Altamirano et al . 2009a ) and { \it 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 { \it HST } imaging , g ^ { \prime } > 22 during the August outburst from Gemini-South GMOS imaging , and J { \lower 3.44 pt \hbox { $ \buildrel > \over { \sim } $ } } 18.5 and K { \lower 3.44 pt \hbox { $ \buildrel > \over { \sim } $ } } 17 during the July outburst from CTIO 4-m ISPI imaging . Archival { \it Chandra } X-ray images of the core do not detect the quiescent counterpart ( L _ { X } < 1 - 2 \times 10 ^ { 31 } ergs s ^ { -1 } ) , and place a bolometric luminosity limit of L _ { NS } < 6 \times 10 ^ { 31 } ergs s ^ { -1 } ( one of the lowest measured ) for a hydrogen atmosphere neutron star . A short { \it Chandra } observation 10 days into quiescence found two photons at NGC 6440 X-2 ’ s position , suggesting enhanced quiescent emission at L _ { X } \sim 6 \times 10 ^ { 31 } ergs s ^ { -1 } . NGC 6440 X-2 currently shows the shortest recurrence time ( \sim 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 .