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.
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