  An expression of partial wave expansion of three-baryon interactions in
chiral effective field theory is presented. The derivation follows the method
by Hebeler et al. [Phys. Rev. C{\bf 91}, 044001 (2015)], but the final
expression is more general. That is, a systematic treatment of the higher-rank
spin-momentum structure of the interaction becomes possible. Using the derived
formula, a $\Lambda$-deuteron folding potential is evaluated. This information
is valuable for inferring the possible contribution of the $\Lambda NN$
three-baryon forces to the hypertriton as the basis of further studies by
sophisticated Faddeev calculations. A microscopic understanding of $\Lambda NN$
three-baryon forces together with two-body $\Lambda N$ interactions is
essential for the description of hypernuclei and neutron-star matter.
