  For the special case of freely evolving Dirac electrons in $1 + 1$
dimensions, Feynman checkerboard paths have previously been used to derive
Wigner's arrival-time distribution which includes all arrivals. Here, an
attempt is made to use these paths to determine the corresponding distribution
of first-arrival times. Simple analytic expressions are obtained for the
relevant components of the first-arrival propagator. These are used to
investigate the relative importance of the first-arrival contribution to the
Wigner arrival-time distribution and of the contribution arising from
interference between first and later (i.e. second, third, ...) arrivals. It is
found that a distribution of (intrinsic) first-arrival times for a Dirac
electron cannot in general be consistently defined using checkerboard paths,
not even approximately in the nonrelativistic regime.
