  The occurrence of charge-density-wave (CDW) order is a common thread in the
phase diagram of cuprate high-transition-temperature ($T_c$) superconductors.
In iron-based superconductors (FeSCs), nematic order and fluctuations play a
decisive role in driving other emergent orders. CDW order has been observed by
scanning tunneling microscopy for various FeSCs such as FeSe thin films,
uniaxially strained LiFeAs, and tetragonal FeSe$_{0.81}$S$_{0.19}$. However, it
remains elusive if the CDW in these materials is a bulk phenomenon as well as
if and how it intertwines with the electronic nematicity. Using energy-resolved
resonant X-ray scattering at the Fe-L$_3$ edge, we report the discovery of a
local-strain-induced incommensurate isotropic CDW order in
FeSe$_{0.82}$S$_{0.18}$. A highly anisotropic CDW response under uniaxial
strain unambiguously manifests that the CDW is directly coupled to the
nematicity. Transforming part of Fe$^{2+}$ to Fe$^{3+}$ on the surface of
FeSe$_{1-x}$S$_{x}$ reveals that the same isotropic CDW can be induced,
enhanced, and stabilized in the whole nematic regime measured ($x=0-0.19$). As
Fe$^{3+}$ can create local lattice distortions on the surface, the CDW could
arise from the interaction between the local strain around Fe$^{3+}$ and the
nematic electron correlations. Our experimental observation of a
local-strain-induced CDW gives vital information for understanding the
interplay between electron correlations and the electronic nematicity in FeSCs.
