This paper studies the consequences of parallel import (PI) on process innovation of firms heterogeneous in their production technology. In an international setting where foreign markets differ with respect to their intellectual property rights regime, a move by a technologically inferior firm to exploit a new unregulated market can result in imitation and PI. The impact of PI on innovation is determined by the degree of heterogeneity between firms and trade costs. Increasing trade costs shifts from the market share losses brought by PI from the more to the less productive firm. This induces the former to invest more in R&D. At this point, sales in the foreign market become a determinant of the R&D decision by the technologically inferior firm. For low levels of firm heterogeneity, PI increases output by this firm targeted for the unregulated market, hence increases its innovation efforts. A tariff policy accompanied by opening borders to PI only increases welfare when the technological gap between the two firms is sufficiently large.