This paper investigates optimal capital taxation in an innovation-driven growth model. We examine how the optimal capital tax rate varies with externalities associated with R&D and innovation. Our results show that the optimal capital tax rate is higher when (i) the “stepping on toes effect” is smaller, (ii) the “standing on shoulders effect” is stronger, or (iii) the extent of creative destruction is smaller. The optimal capital tax rate is more likely to be positive when there is underinvestment in R&D. Moreover, the optimal capital tax rate and the monopolistic markup exhibit an inverted-U relationship. By calibrating our model to the US economy, we find that the optimal capital tax rate is positive, at a rate of around 6.6%. Finally, we consider a number of extensions and find that the result of a positive optimal capital tax is robust.