We present a first-principles study of spin-dependent electron transport through gold nanochains suspended between cobalt electrodes aimed at elucidating the electronic origin of the high magnetoresistance recently observed experimentally in such nanojunctions. Our nonequilibrium Green's function based calculations confirm the occurrence of high spin polarization of conductance in Co/Au/Co nanocontacts, which in some cases reaches 90 per cent. Our analysis allows to relate such behavior to the hybridization of electronic orbitals of neighboring cobalt and gold atoms of the nanocontact. The results obtained give clear evidence of the presence of spin injection from Co electrodes into paramagnetic gold contacts.