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 dataset collected through 2014 using the same parametric foreground modeling as in the previous analysis. From simulations, we find that the uncertainty on r is reduced by ∼10 %, from σ (r )=0.024 to 0.022, which can be compared with a ∼26 % reduction obtained when using a perfect lensing template or if there were zero lensing B -modes. Applying the technique to the real data, the constraint on r is improved from r0.05<0.090 to r0.05<0.082 (95% C.L.). This is the first demonstration of improvement in an r constraint through delensing.