A single-component conducting molecular crystal composed of paramagnetic copper complexes, [Cu(dmdt)2]0+, was prepared. The crystal has an unprecedented three-dimensionally packed molecular arrangement and exhibits a fairly high conductivity (1 S cm-1 at room temperature). The magnetic susceptibility measurements revealed that [Cu(dmdt)2]0+ molecule keeps most of S = 1/2 spin moments. The difference of the bond lengths between [Cu(dmdt)2]0+ and [Cu(dmdt)2]2- is consistent with the result of the molecular orbital calculation.