This is the author accepted manuscript. The final version is available from AAAS via http://dx.doi.org/10.1126/science.aab1910Gravitational waves are expected to be radiated by supermassive black hole binaries formed during galaxy mergers. A stochastic superposition of gravitational waves from all such binary systems would modulate the arrival times of pulses from radio pulsars. Using observations of millisecond pulsars obtained with the Parkes radio telescope, we constrained the characteristic amplitude of this background, A(c,yr), to be <1.0 × 10(-15) with 95% confidence. This limit excludes predicted ranges for A(c,yr) from current models with 91 to 99.7% probability. We conclude that binary evolution is either stalled or dramatically accelerated by galactic-center environments and that higher-cadence and shorter-wavelength observations would be more sensitive to gravitational waves.The PPTA project was initiated with support from R.N.M.’s Australian Research Council (ARC) Federation Fellowship (grant FF0348478) and from CSIRO under that fellowship program. The PPTA project has also received support from ARC through Discovery Project grants DP0985272 and DP140102578. N.D.R.B. acknowledges support from a Curtin University research fellowship. G.H. and Y.L. are recipients of ARC Future Fellowships (respectively, grants FT120100595 and FT110100384). S.O. is supported by the Alexander von Humboldt Foundation. R.M.S. acknowledges travel support from CSIRO through a John Philip Award for excellence in early-career research. The authors declare no conflicts of interest. Data used in this analysis can be accessed via the Australian National Data Service (www.ands.org.au)