  Recent non-detection of gravitational-wave backgrounds from pulsar timing
arrays casts further uncertainty on the evolution of supermassive black hole
binaries. We study the capabilities of current gravitational-wave observatories
to detect individual binaries and demonstrate that, contrary to conventional
wisdom, some are in principle detectable throughout the Universe. In
particular, a binary with rest-frame mass $\gtrsim10^{10}\,M_\odot$ can be
detected by current timing arrays at arbitrarily high redshifts. The same claim
will apply for less massive binaries with more sensitive future arrays. As a
consequence, future searches for nanohertz gravitational waves could be
expanded to target evolving high-redshift binaries. We calculate the maximum
distance at which binaries can be observed with pulsar timing arrays and other
detectors, properly accounting for redshift and using realistic binary
waveforms.
