This paper studies the implications of technical progress through investment-specific technical change in a business cycle model with search and matching  frictions and endogenous job destruction. The interaction between the capital formation needed to reap the benefits of an investment-specific technology shock and gradual labor-market matching, generates hump-shaped, persistent responses in output, vacancies, and unemployment. The endogenous job destruction decision also leads to small but persistent endogenous fluctuations in total factor productivity. Simulations suggest a limited role for investment-specific technology shocks as a source of business cycle fluctuations compared to a standard real business cycle model.