In July 2011, observations of a massive phytoplankton bloom in the ice‐covered waters of the western Chukchi Sea raised questions about the extent and frequency of under‐ice phytoplankton growth and its contribution to the carbon budget in the Arctic Ocean. To address some of these questions, we use the fully‐coupled, high‐resolution Regional Arctic System Model to simulate Arctic marine biogeochemistry over a 30‐year period. Our results demonstrate the presence of extensive under‐ice phytoplankton growth in the western Arctic (WA) in summer. In addition, similar growth, yet of lower magnitude, occurs annually in the eastern Arctic (EA). We investigate the critical levels of nitrate concentration and photosynthetically available radiation (PAR) that are necessary for under‐ice phytoplankton growth to occur. Our results show that while the majority of ice‐covered Arctic waters have sufficient surface nitrate levels to sustain growth, PAR reaching the ocean surface through the sea ice in early summer only exceeds critical levels in the WA. We therefore conclude that the EA high chlorophyll‐a concentrations shown in our simulations did not develop under sea ice, but were instead, at least in part, formed in open waters upstream and subsequently advected by ocean currents beneath the sea ice.