  We present measurements of the intensity of the Cosmic X-ray Background (CXB)
with the NuSTAR telescope in the 3-20 keV energy range. Our method uses spatial
modulation of the CXB signal on the NuSTAR detectors through the telescope's
side aperture. Based on the NuSTAR observations of selected extragalactic
fields with a total exposure of 7 Ms, we have estimated the CXB 3-20 keV flux
to be 2.8E-11 erg/s/cm^2/deg^2, which is ~8 higher than measured with HEAO-1
and consistent with the INTEGRAL measurement. The inferred CXB spectral shape
in the 3-20 keV energy band is consistent with the canonical model of Gruber et
al. We demonstrate that the spatially modulated CXB signal measured by NuSTAR
is not contaminated by systematic noise and is limited by photon statistics.
The measured relative scatter of the CXB intensity between different sky
directions is compatible with cosmic variance, which opens new possibilities
for studying CXB anisotropy over the whole sky with NuSTAR.
