  The nature of superconductivity in BiS$_2$-based superconductors has been
controversial while ab-initio calculations proposed this system in close
proximity to a charge-density-wave (CDW) phase. Using high-energy high-flux
X-ray diffraction, we reveal an intrinsic and long-range CDW phase coexisting
with superconductivity in NdO$_{1-x}$F$_{x}$BiS$_2$ superconductor ($x$ = 0.37
and 0.3). The CDW wavevector in NdO$_{0.63}$F$_{0.37}$BiS$_2$ correspond
Q$_{\rm{CDW}}$ = (0.17, 0.17, 0.5) and is associated with transverse atomic
displacements. Interestingly, this wavevector does not match theoretical
expectations based on either phonon softening or Fermi surface nesting. In
NdO$_{0.7}$F$_{0.3}$BiS$_2$, where the superconducting transition temperature
is highest, the CDW satellites are slightly broader and weaker compared to
NdO$_{0.63}$F$_{0.37}$BiS$_2$, possibly suggesting the competition with the
superconductivity. Lastly, we measure a thermal diffuse scattering across the
superconducting transition temperature and find no meaningful changes in favor
of the unconventional pairing mechanism. Our result suggests the importance of
understanding CDW which might hold a key to the superconductivity in the
BiS$_2$-based superconductor.
