  We present a constraint on the tensor-to-scalar ratio, $r$, derived from
measurements of cosmic microwave background (CMB) polarization $B$-modes with
"delensing," whereby the uncertainty on $r$ contributed by the sample variance
of the gravitational lensing $B$-modes is reduced by cross-correlating against
a lensing $B$-mode template. This template is constructed by combining an
estimate of the polarized CMB with a tracer of the projected large-scale
structure. The large-scale-structure tracer used is a map of the cosmic
infrared background derived from Planck satellite data, while the polarized CMB
map comes from a combination of South Pole Telescope, BICEP/Keck, and Planck
data. We expand the BICEP/Keck likelihood analysis framework to accept a
lensing template and apply it to the BICEP/Keck data set collected through 2014
using the same parametric foreground modelling as in the previous analysis.
From simulations, we find that the uncertainty on $r$ is reduced by $\sim10\%$,
from $\sigma(r)$= 0.024 to 0.022, which can be compared with a $\sim26\%$
reduction obtained when using a perfect lensing template. Applying the
technique to the real data, the constraint on $r$ is improved from $r_{0.05} <
0.090$ to $r_{0.05} < 0.082$ (95\% C.L.). This is the first demonstration of
improvement in an $r$ constraint through delensing.
