  Usually, a left-moving fermion in d=1+1 dimensions reflects off a boundary to
become a right-moving fermion. This means that, while overall fermion parity
$(-1)^F$ is conserved, chiral fermion parity for left- and right-movers
individually is not. Remarkably, there are boundary conditions that do preserve
chiral fermion parity, but only when the number of Majorana fermions is a
multiple of 8. In this paper we classify all such boundary states for $2N$
Majorana fermions when a $U(1)^N$ symmetry is also preserved. The fact that
chiral-parity-preserving boundary conditions only exist when $2N$ is divisible
by 8 translates to an interesting property of charge lattices. We also classify
the enhanced continuous symmetry preserved by such boundary states. The state
with the maximum such symmetry is the $SO(8)$ boundary state, first constructed
by Maldacena and Ludwig to describe the scattering of fermions off a monopole
