This paper studies the impact of long-run productivity growth on job finding and separation rates, and thus the unemployment rate, using a search and matching model. We incorporate disembodied technological progress and on-the-job search into the endogenous job separation model of Mortensen and Pissarides (1994). The incorporation of on-the-job search allows faster growth to reduce unemployment by decreasing the separation rate and inducing job creation. We demonstrate that introducing on-the-job search substantially improves the ability of the Mortensen and Pissarides model to explain the impact of growth on unemployment. Our quantitative analysis shows that our model increases the magnitude of the negative impact of growth on unemployment compared to the standard matching model with disembodied technological progress.