  Moir\'e patterns can lead to fundamentally new electronic behavior when
formed between two atomic lattices slightly shifted with respect to each other.
A solid is however not just characterized by the atomic lattice, but also by
charge or magnetic excitations that do not need to be commensurate to the
lattice. This raises the question if one can obtain a moir\'e by combining
periodic electronic modulations and the atomic lattice. Here we report on the
discovery of a one-dimensional charge density wave (1D-CDW) which is a moir\'e
pattern between the atomic lattice and a hot spot for electronic scattering in
the bandstructure of the hidden order (HO) state of URu$_2$Si$_2$. The moir\'e
is produced by fracturing the crystal at low temperatures. Our results suggest
that charge interactions are among the most relevant features competing with HO
in URu$_2$Si$_2$.
