  We consider the entanglement between two spatial subregions in the
Lieb-Liniger model of bosons in one spatial dimension interacting via a contact
interaction. Using ground state path integral quantum Monte Carlo we
numerically compute the R\'{e}nyi entropy of the reduced density matrix of the
subsystem as a measure of entanglement. Our numerical algorithm is based on a
replica method previously introduced by the authors, which we extend to
efficiently study the entanglement of spatial subsystems of itinerant bosons.
We confirm a logarithmic scaling of the R\'{e}nyi entropy with subsystem size
that is expected from conformal field theory, and compute the non-universal
subleading constant for interaction strengths ranging over two orders of
magnitude. In the strongly interacting limit, we find agreement with the known
free fermion result.
