  Gravitational 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 will modulate the arrival
times of pulses from radio pulsars. Using observations of millisecond pulsars
obtained with the Parkes radio telescope, we constrain the characteristic
amplitude of this background, $A_{\rm c,yr}$, to be < $1.0\times10^{-15}$ with
95% confidence. This limit excludes predicted ranges for $A_{\rm c,yr}$ from
current models with 91-99.7% 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 result in an
increased sensitivity to gravitational waves.
