Geoengineering might manipulate Earths climate in order to counteract global warming fromanthropogenic greenhouse gas emissions. We investigate in detail the potential of a specificgeoengineering technique: carbon sequestration by artificially enhanced silicate weathering via the dissolution of olivine. This approach would not only operate against rising temperatures but would also counteract ocean acidification, because it influences the global climate via the carbon cycle.We here show the consequences of this technique for the chemistry of the surface ocean at rates necessary for geoengineering. We calculate that olivine dissolution has the potential tosequestrate up to 1 Pg C yr-1 directly, if olivine is distributed as fine powder over land areas of the humid tropics. The carbon sequestration potential in soils is limited by the saturation concentration of silicic acid. In our calculations for the Amazon and Congo river catchments, a maximum annual dissolution of 1.8 and 0.4 Pg of olivine seems possible, corresponding to the sequestration of 0.5 and 0.1 Pg C yr-1. Open water dissolution of fine grained olivine and an enhancement of the biological pump by the rising riverine input of silicic acid might increase our estimate of the carbon sequestration, but additional research is needed here. We finally calculate with a carbon cycle model the consequences of sequestration rates of 1 to 5 Pg C yr-1 for the 21st century by this technique. At maximum, enhanced weathering of olivine powder in the humid tropics could reduce global warming by 1 K and counteract ocean acidification by a rise in surface ocean pH by 0.1 in the year 2100.