  The $\Lambda_c^+K^-$ mass spectrum is studied with a data sample of $pp$
collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated
luminosity of 5.6 fb$^{-1}$ collected by the LHCb experiment. Three $\Xi_c^0$
states are observed with a large significance and their masses and natural
widths are measured to be \begin{eqnarray*} m(\Xi_c(2923)^0)&=& 2923.04 \pm
0.25 \pm 0.20 \pm 0.14 ~\mathrm{MeV}, \Gamma(\Xi_c(2923)^0) &=& 7.1 \pm 0.8 \pm
1.8 ~\mathrm{MeV}, \end{eqnarray*} \begin{eqnarray*} m(\Xi_c(2939)^0) &=&
2938.55 \pm 0.21 \pm 0.17 \pm 0.14 ~\mathrm{ MeV}, \Gamma(\Xi_c(2939)^0) &=&
10.2 \pm 0.8 \pm 1.1 ~\mathrm{ MeV}, \end{eqnarray*} \begin{eqnarray*}
m(\Xi_c(2965)^0) &=& 2964.88 \pm 0.26 \pm 0.14 \pm 0.14~\mathrm{ MeV},
\Gamma(\Xi_c(2965)^0) &=& 14.1 \pm 0.9 \pm 1.3~\mathrm{ MeV}, \end{eqnarray*}
where the uncertainties are statistical, systematic, and due to the limited
knowledge of the $\Lambda_c^+$ mass. The $\Xi_c(2923)^0$ and $\Xi_c(2939)^0$
baryons are new states. The $\Xi_c(2965)^0$ state is in the vicinity of the
known $\Xi_c(2970)^0$ baryon; however, their masses and natural widths differ
significantly.
