  We present muon spin rotation measurements on superconducting Cu intercalated
Bi$_2$Se$_3$, which was suggested as a realization of a topological
superconductor. We observe a clear evidence of the superconducting transition
below 4 K, where the width of magnetic field distribution increases as the
temperature is decreased. The measured broadening at mK temperatures suggests a
large London penetration depth in the $ab$ plane ($\lambda_{\mathrm{eff}}\sim
1.6$ $\mathrm{\mu}$m). We show that the temperature dependence of this
broadening follows the BCS prediction, but could be consistent with several gap
symmetries.
