This invention provides a method for preparing cerium oxide nanoparticles with a narrow size distribution. The cerium oxide nanoparticles obtained by the method of the invention are nearly all crystalline. The method comprises providing a first aqueous solution comprising cerium nitrate and providing a second aqueous solution comprising hexamethylenetetramine. The first and second aqueous solutions are mixed to form a mixture, and the mixture is maintained at a temperature no higher than about 320.degree. K to form nanoparticles. The nanoparticles that are formed are then separated from the mixture. A further aspect of the present invention is an apparatus for preparing cerium oxide nanoparticles. The apparatus comprises a mixing vessel having a first compartment for holding a first aqueous solution comprising cerium nitrate and a second compartment for holding a second aqueous solution comprising hexamethylenetetramine. The mixing vessel has a retractable partition separating the first and second compartments.