We examine six different coupled climate model simulations to determine the ocean biological response to climate warming between the beginning of the industrial revolution and 2050. We use vertical velocity, maximum winter mixed layer depth, and sea ice cover to define six biomes. Climate warming leads to a contraction of the highly productive marginal sea ice biome by 42% in the Northern Hemisphere and 17% in the Southern Hemisphere, and leads to an expansion of the low productivity permanently stratified subtropical gyre biome by 4.0% in the Northern Hemisphere and 9.4% in the Southern Hemisphere. In between these, the subpolar gyre biome expands by 16% in the Northern Hemisphere and 7% in the Southern Hemisphere, and the seasonally stratified subtropical gyre contracts by 11% in both hemispheres. The low-latitude (mostly coastal) upwelling biome area changes only modestly. Vertical stratification increases, which would be expected to decrease nutrient supply everywhere, but increase the growing season length in high latitudes. We use satellite ocean color and climatological observations to develop an empirical model for predicting chlorophyll from the physical properties of the global warming simulations. Four features stand out in the response to global warming: (1) a drop in chlorophyll in the North Pacific due primarily to retreat of the marginal sea ice biome, (2) a tendency toward an increase in chlorophyll in the North Atlantic due to a complex combination of factors, (3) an increase in chlorophyll in the Southern Ocean due primarily to the retreat of and changes at the northern boundary of the marginal sea ice zone, and (4) a tendency toward a decrease in chlorophyll adjacent to the Antarctic continent due primarily to freshening within the marginal sea ice zone. We use three different primary production algorithms to estimate the response of primary production to climate warming based on our estimated chlorophyll concentrations. The three algorithms give a global increase in primary production of 0.7% at the low end to 8.1% at the high end, with very large regional differences. The main cause of both the response to warming and the variation between algorithms is the temperature sensitivity of the primary production algorithms. We also show results for the period between the industrial revolution and 2050 and 2090.