We examine the relationship between competition and innovation in an industry where production is polluting and R&D aims to reduce emissions ("green" innovation). We present an n-firm oligopoly where firms compete in quantities and decide their investment in "green" R&D. When environmental taxation is exogenous, aggregate R&D investment always increases with the number of firms in the industry. Next we analyse the case where the emission tax is set endogenously by a regulator (committed or time-consistent) with the aim to maximise social welfare. We show that an inverted-U relationship exists between aggregate R&D and industry size under reasonable conditions, and is driven by the presence of R&D spillovers.