We have carried out an investigation of surface structures of Cr nanoparticles grown on a MgO layer for studying single electron tunneling (SET). Reflection high-energy electron diffraction pattern changes from spotty to streak with decreasing Cr nominal thickness, while Cr forms nano size particles with the size of around 3.5 nm in diameter for all the samples. The double tunnel junctions for the Cr nominal thickness of 0.1 nm show clear Coulomb blockade with the threshold voltage of 50 mV, indicating that this Cr nanoparticle satisfies the condition for the appearance of SET. The relatively large volume of the Cr nanoparticles may be related with the fact that tunnel magnetoresistance due to spin accumulation in Cr nanoparticles is small.