  We present the resummation of one-jettiness for the colour-singlet plus jet
production process $p p \to ( \gamma^*/Z \to \ell^+ \ell^-) + {\text{jet}}$ at
hadron colliders up to the fourth logarithmic order (N$^3$LL). This is the
first resummation at this order for processes involving three coloured partons
at the Born level. We match our resummation formula to the corresponding
fixed-order predictions, extending the validity of our results to regions of
the phase space where further hard emissions are present. This result paves the
way for the construction of next-to-next-to-leading order simulations for
colour-singlet plus jet production matched to parton showers in the GENEVA
framework.
