  We point out that each of the error boxes of the two highest-energy
cosmic-ray shower events known, overlaps with that of a strong gamma-ray burst
(GRB). The GRBs precede the cosmic rays by 5.5, and 11 months respectively. In
one case the strongest known cosmic ray is paired with the strongest gamma-ray
burst in the BATSE catalogue. The probability of this to have occurred by
chance seems rather small. Without building on post-factum statistics, we think
the above is remarkable enough to suggest that the cosmic ray and gamma-ray
burst were produced by the same outburst. A time delay (and a small positional
disparity) is expected, since the trajectory of a charged cosmic-ray particle
is wriggled by intervening magnetic fields. We estimate that the Galaxy's field
alone may produce a delay of the order observed. We discuss some of the
implications that follow if such an association is confirmed. For example, the
upper limit on the distance to the cosmic-ray source, combined with a
much-better-determined position of the gamma-ray burst source, narrows greatly
the volume in which to look for an optical counterpart. There is also useful
information in the time delay regarding, e.g., intergalactic magnetic fields.
