  The layered bismuth oxy-sulfide materials, which are structurally related to
the Fe-pnictides/chalcogenides and cuprates superconductors, have brought
substantial attention for understanding the physics of reduced dimensional
superconductors. We have examined the pairing symmetry of recently discovered
BiCh$_2$-based superconductor, La$_\mathrm{1-x}$Ce$_\mathrm{x}$OBiSSe with $x$
= 0.3, through transverse field (TF) muon spin rotation measurement, in
addition we present the results of magnetization, resistivity and zero field
(ZF) muon spin relaxation measurements. Bulk superconductivity has been
observed below 2.7 K for $x$ = 0.3, verified by resistivity and magnetization
data. The temperature dependence of the magnetic penetration depth has been
determined from TF-$\mu$SR data can be described by an isotropic two-gap $s+s$
wave model compared to a single gap $s$- or anisotropic $s$-wave models, the
resemblance with Fe-pnictides/chalcogenides and MgB$_2$. Furthermore, from the
TF-$\mu$SR data, we have determined the London's penetration depth
$\lambda_\mathrm{L}(0)$ = 452(3) nm, superconducting carrier's density
$n_\mathrm{s}$ = 2.18(1) $\times$10$^{26}$ carriers/m$^{3}$ and effective mass
enhancement $m^{*}$ = 1.66(1) $m_\mathrm{e}$, respectively. No signature of
spontaneous internal field is found down to 100 mK in ZF-$\mu$SR measurement
suggest that time-reversal symmetry is preserved in this system.
