The total cross section for the dd -> 4He K+ K- reaction has been measured at a beam momentum of 3.7 GeV/c, corresponding to an excess energy of 39 MeV, which is the maximum possible at the Cooler Synchrotron COSY-J{u}lich. A deuterium cluster-jet target and the ANKE forward magnetic spectrometer, placed inside the storage ring, have been employed in this investigation. We find a total cross section of sigma(tot) < 14 pb, which brings into question the viability of investigating the dd -> 4He a0(980) reaction as a means of studying isospin violation.