  The optical light curve of the quasar PG 1302-102 at $z = 0.278$ shows a
strong, smooth 5.2 yr periodic signal, detectable over a period of $\sim 20$
yr. Although the interpretation of this phenomenon is still uncertain, the most
plausible mechanisms involve a binary system of two supermassive black holes
with a subparsec separation. At this close separation, the nuclear black holes
in PG 1302-102 will likely merge within $\sim 10^{5}$ yr due to gravitational
wave emission alone. Here we report the rest-frame near-infrared time lags for
PG 1302-102. Compiling data from {\it WISE} and {\it Akari}, we confirm that
the periodic behavior reported in the optical light curve from Graham et al.
(2015) is reproduced at infrared wavelengths, with best-fit observed-frame 3.4
and $4.6 \mu$m time lags of $(2219 \pm 153, 2408 \pm 148)$ days for a near
face-on orientation of the torus, or $(4103\pm 153, 4292 \pm 148)$ days for an
inclined system with relativistic Doppler boosting in effect. The periodicity
in the infrared light curves and the light-travel time of the accretion disk
photons to reach the dust glowing regions support that a source within the
accretion disk is responsible for the optical variability of PG 1302-102,
echoed at the further out dusty regions. The implied distance of this dusty,
assumed toroidal region is $\sim$ 1.5 pc for a near face-on geometry, or
$\sim$1.1 pc for the relativistic Doppler boosted case.
