Large Igneous Provinces (LIPs) are associated with the largest climate perturbations in Earth's history. The North Atlantic Igneous Province (NAIP) and Paleocene-Eocene Thermal Maximum (PETM) constitute an exemplar of this association. As yet we have no means to reconstruct the pacing of LIP greenhouse gas emissions for comparison with climate records at millennial resolution. Here, we calculate carbon-based greenhouse gas fluxes associated with the NAIP at sub-millennial resolution by linking measurements of the mantle convection process that generated NAIP magma with observations of the individual geological structures that controlled gas emissions in a Monte Carlo framework. These simulations predict peak emissions flux of 0.2-0.5 PgC yr-1 and show that the NAIP could have initiated PETM climate change. This is the first predictive model of carbon emissions flux from any proposed PETM carbon source that is directly constrained by observations of the geological structures that controlled the emissions.