  Periodically driven systems often exhibit behavior distinct from static
systems. In single-particle, static systems, any amount of disorder generically
localizes all eigenstates in one dimension. In contrast, we show that in
topologically non-trivial, single-particle Floquet loop drives with chiral
symmetry in one dimension, a localization-delocalization transition occurs as
the time $t$ is varied within the driving period ($0 \le t \le
T_\text{drive}$). We find that the time-dependent localization length
$L_\text{loc}(t)$ diverges with a universal exponent as $t$ approaches the
midpoint of the drive: $L_\text{loc}(t) \sim (t - T_\text{drive}/2)^{-\nu}$
with $\nu=2$. We provide analytical and numerical evidence for the universality
of this exponent within the AIII symmetry class.
