Surface waters of the eastern equatorial Pacific Ocean present the enigma of apparently high plant-nutrient concentrations but low phytoplankton biomass and productivity. One explanation for this `high-nitrate, low-chlorophyll' (HNLC) phenomenon has been that growth is limited by iron availability,. Here we use field data and a simple silicon-cycle model to investigate the HNLC condition for the upwelling zone of this ocean region. Measured silicate concentrations in surface waters are low and largely invariant with time, and set the upper limit on the total possible biological utilization of dissolved inorganic carbon. Chemical and biological data from surface waters indicate that diatoms-silica-shelled phytoplankton-carry out all the `new production' (nitrate uptake). Smaller phytoplankton (picoplankton) accomplish most of the total primary production, largely fuelled by nitrogen regenerated in reduced forms as a result of grazing by zooplankton. The model predicts values of new and export production (the production exported to below the euphotic zone) that compare well with measured values. New and export production are in balance for biogenic silica, whereas new production exceeds export for nitrogen. The HNLC condition in the upwelling zone can therefore be understood to be due to a chemostat-like regulation of nitrate uptake by upwelled silicate supply to diatoms: `low-silicate HNLC'. These results are not inconsistent with observations of iron-fertilized diatom growth during in situ experiments in `low-iron HNLC' waters outside this upwelling zone,, but reflect the role of different supply rates of iron and silicate in determining the nature of the HNLC condition.