This paper studies the effect of top tax rates on inventors' mobility since 1977. We put special emphasis on "superstar" inventors, those with the most and most valuable patents. We use panel data on inventors from the United States and European Patent Offices to track inventors' locations over time and combine it with international effective top tax rate data. We construct a detailed set of proxies for inventors' counterfactual incomes in each possible destination country including, among others, measures of patent quality and technological fit with each potential destination. We find that superstar top 1% inventors are significantly affected by top tax rates when deciding where to locate. The elasticity of the number of domestic inventors to the net-of-tax rate is relatively small, between 0.04 and 0.06, while the elasticity of the number of foreign inventors is much larger, around 1.3. The elasticities to top net-of-tax rates decline as one moves down the quality distribution of inventors. Inventors who work in multinational companies are more likely to take advantage of tax differentials. On the other hand, if the company of an inventor has a higher share of its research activity in a given country, the inventor is less sensitive to the tax rate in that country.