  We present initial results and the source catalog from the NuSTAR survey of
the Extended Chandra Deep Field South (hereafter, ECDFS) - currently the
deepest contiguous component of the NuSTAR extragalactic survey program. The
survey covers the full ~30 arcmin x 30 arcmin 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/cm2/s (3-8 keV), ~3.4 x 10^-14
erg/cm2/s (8-24 keV) and ~3.0 x 10^-14 erg/cm2/s (3-24 keV). Fifty four (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 keV to 3-8 keV band
ratios of the twelve sources that are detected in both bands span the range
0.39-1.7, corresponding to a photon index range of Gamma ~ 0.5-2.3, with a
median photon index of 1.70 +/- 0.52. The redshifts of the 49 sources in our
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(10-40
keV) ~ (0.7-300) x 10^43 erg/s, sampling below the "knee" of the X-ray
luminosity function out to z ~ 0.8-1. Finally, we 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.
