The deformed doubly magic nucleus Hs270 has so far only been observed as the four-neutron (4n) evaporation residue of the reaction Mg26+Cm248, where a maximum cross section of 3 pb was measured. Theoretical studies on the formation of Hs270 in the 4n evaporation channel of fusion reactions with different entrance channel asymmetry in the framework of a two-parameter Smoluchowski equation predict that the reactions Ca48+Ra226 and S36+U238 result in higher cross sections due to lower reaction Q values, in contrast to simple arguments based on the reaction asymmetry, which predict opposite trends. Calculations using hivap predict cross sections for the reaction S36+U238 that are similar to those of the Mg26+Cm248 reaction. Here, we report on the first measurement of evaporation residues formed in the complete nuclear fusion reaction S36+U238 and the observation of Hs270, which is produced in the 4n evaporation channel, with a measured cross section of 0.8-0.7+2.6 pb at 51-MeV excitation energy. The one-event cross-section limits (68% confidence level) for the 3n, 4n, and 5n evaporation channels at 39-MeV excitation energy are 2.9 pb, while the cross-section limits of the 3n and 5n channel at 51 MeV are 1.5 pb. This is significantly lower than the 5n cross section of the Mg26+Cm248 reaction at similar excitation energy. © 2010 The American Physical Society.