This table contains the source catalog from the Nuclear Spectroscopic Telescope Array (NuSTAR) survey of the Extended Chandra Deep Field South (hereafter, ECDFS), that is currently the deepest contiguous component of the NuSTAR extragalactic survey program. The survey covers the full ~30' x 30' area of this field to a maximum depth of ~360 ks (~220 ks when corrected for vignetting at 3 - 24 keV), reaching sensitivity limits of ~1.3 x 10^-14 erg/s/cm² (3 - 8 keV), ~3.4 x 10^-14 erg/s/cm² (8 - 24 keV), and ~3.0 x 10^-14 erg/s/cm² (3 - 24 keV). A total of 54 sources are detected over the full field, although five of these are found to lie below our significance threshold once contaminating flux from neighboring (i.e., blended) sources is taken into account. Of the remaining 49 that are significant, 19 are detected in the 8 - 24 keV band. The 8 - 24 to 3 - 8 keV band ratios of the 12 sources that are detected in both bands span the range 0.39 - 1.7, corresponding to a photon index (Gamma) range of about 0.5 - 2.3, with a median photon index of 1.70 +/- 0.52. The redshifts of the 49 sources in the main sample span the range z = 0.21 - 2.7, and their rest-frame 10 - 40 keV luminosities (derived from the observed 8 - 24 keV fluxes) span the range L_10-40keV ~ (0.7 - 300) x 10⁴³erg/s, sampling below the "knee" of the X-ray luminosity function out to z ~ 0.8 - 1. Finally, the authors identify one NuSTAR source that has neither a Chandra nor an XMM-Newton counterpart, but that shows evidence of nuclear activity at infrared wavelengths and thus may represent a genuine, new X-ray source detected by NuSTAR in the ECDFS. The NuSTAR ECDFS survey consists of observations from two separate passes. Observations making up the first pass were taken between 2012 September and December, and those making up the second pass were taken roughly six months later, between 2013 March and April. For their cosmological calculations, the authors adopt a Hubble constant H₀ of 71 km s^-1 Mpc ^-1, Omega_M of 0.27, and Omega_Lambda of 0.73. This table was created by the HEASARC in September 2017 based on the <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/ApJ/808/184">CDS Catalog J/ApJ/808/184</a> file catalog.dat. This is a service provided by NASA HEASARC .