  The structure of single-$\Lambda$ hypernuclei is studied using the chiral
hyperon-nucleon potentials derived at leading order (LO) and next-to-leading
order (NLO) by the J\"{u}lich--Bonn--Munich group. Results for the separation
energies of $\Lambda$ single-particle states for various hypernuclei from
$^5_{\Lambda}$He to $^{209}_{\,\,\,\,\,\Lambda}$Pb are presented for the LO
interaction and the 2013 (NLO13) and 2019 (NLO19) versions of the NLO
potentials. It is found that the results based on the LO potential show a clear
tendency for overbinding while those for the NLO13 interaction underbind most
of the considered hypernuclei. A qualitatively good agreement with the data is
obtained for the NLO19 interaction over a fairly large range of mass number
values when considering the uncertainty due to the regulator dependence. A
small spin-orbit splitting of the $p$-, $d$-, $f$-, and $g$-wave states is
predicted by all interactions, in line with the rather small values observed in
pertinent experiments.
