We present a simple formalism for the evolution of timelike jets in which tree-level matrix-element corrections can be systematically incorporated, up to arbitrary parton multiplicities and over all of phase space, in a way that exponentiates the matching corrections. The scheme is cast as a shower Markov chain which generates one single unweighted event sample, that can be passed to standard hadronization models. Remaining perturbative uncertainties are estimated by providing several alternative weight sets for the same events, at a relatively modest additional overhead. As an explicit example, we consider Z→qq̄ evolution with unpolarized, massless quarks and include several formally subleading improvements as well as matching to tree-level matrix elements through αs4. The resulting algorithm is implemented in the publicly available Vincia plugin to the Pythia 8 event generator. The plug-in is available from the web site: http://projects.hepforge.org/vincia/.