We report here the results of magnetic susceptibility, electrical-resistivity, magnetoresistance (MR), heat-capacity and 151 Eu Mössbauer effect measurements on the compound, Eu2CuSi3, crystallizing in an AlB2-derived hexagonal structure. The results establish that Eu ions are divalent, undergoing long-range ferromagnetic-ordering below (TC =) 37 K. An interesting observation is that the sign of MR is negative even at temperatures close to 3TC , with increasing magnitude with decreasing temperature exhibiting a peak at TC . This observation, being made for a Cu containing magnetic rare-earth compound for the first time, is of relevance to the field of collosal magnetoresistance.