  We construct an exactly solvable lattice model for a deconfined quantum
critical point (DQCP) in (1+1) dimensions. This DQCP occurs in an unusual
setting, namely at the edge of a (2+1) dimensional bosonic symmetry protected
topological phase (SPT) with $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. The
DQCP describes a transition between two gapped edges that break different
$\mathbb{Z}_2$ subgroups of the full $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry.
Our construction is based on an exact mapping between the SPT edge theory and a
$\mathbb{Z}_4$ spin chain. This mapping reveals that DQCPs in this system are
directly related to ordinary $\mathbb{Z}_4$ symmetry breaking critical points.
