As part of our campaign to determine the nature of the various source populations of the low-luminosity globular cluster X-ray sources, we have obtained a Chandra X-ray Observatory ACIS-S3 image of the globular cluster NGC 6440. We detect 24 sources to a limiting luminosity of ∼2 × 1031 erg s−1 (0.5–2.5 keV) inside the cluster’s half-mass radius, all of which lie within ∼2 core radii of the cluster center. We also find excess emission in and around the core which could be due to unresolved point sources. Based upon X-ray luminosities and colors, we conclude that there are 4–5 likely quiescent low-mass X-ray binaries and that most of the other sources are cataclysmic variables. We compare these results to Chandra results from other globular clusters and find the X-ray luminosity functions differ among the clusters. Subject headings: globular clusters: individual (NGC 6440) — stars: neutron — cataclysmic variables — binaries: close Center for Space Research and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307; davep@space.mit.edu, lewin@space.mit.edu, jmm@space.mit.edu Astronomical Institute, Utrecht University, PO Box 80 000, 3508 TA Utrecht, The Netherlands; F.W.M.Verbunt@astro.uu.nl Astronomy Department, Box 351580, University of Washington, Seattle, WA 98195; homer@astro.washington.edu Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218; margon@stsci.edu Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; bgaensler@cfa.harvard.edu Department of Physics, Rutherford Physics Building, McGill University, 3600 University Street, Montreal, QC H3A 2T8, Canada; vkaspi@physics.mcgill.ca Astronomy Department, California Institute of Technology, Mail Code 105-24, Pasadena, CA 91125; derekfox@astro.caltech.edu Astronomical Institute “Anton Pannekoek,” University of Amsterdam and Center for High-Energy Astrophysics, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands; michiel@astro.uva.nl