  We report measurements of the London penetration depth [$\Delta\lambda(T)$]
of the recently discovered iron-based superconductor (Li$_{1-x}$Fe$_x$)OHFeSe,
in order to characterize the nature of the superconducting gap structure. At
low temperatures, $\Delta\lambda(T)$ displays nearly temperature independent
behavior, indicating a fully open superconducting gap. We also analyze the
superfluid density $\rho_s(T)$ which cannot be well accounted for by a
single-gap isotropic $s$-wave model but are consistent with either two-gaps, a
model for the orbital selective $s\times\tau_3$ state or anisotropic $s$-wave
superconductivity.
