We present near-infrared H and K-band spectro-interferometric observations of the gaseous disk around the primary Be star in the delta Sco binary system, obtained in 2007 (between periastron passages in 2000 and 2011). Observations using the CHARA/MIRC instrument at H-band resolve an elongated disk with a Gaussian FWHM 1.18 x 0.91 mas. Using the Keck Interferometer, the source of the K-band continuum emission is only marginally spatially resolved, and consequently we estimate a relatively uncertain K-band continuum disk FWHM of 0.7 +/- 0.3 mas. Line emission on the other hand, He1 (2.0583 micron) and Br gamma (2.1657 micron), is clearly detected, with about 10% lower visibilities than those of the continuum. When taking into account the continuum/line flux ratio this translates into much larger sizes for the line emission regions: 2.2 +/- 0.4 mas and 1.9 +/- 0.3 mas for He1 and Br gamma respectively. Our KI data also reveal a relatively flat spectral differential phase response, ruling out significant off-center emission. We expect these new measurements will help constrain dynamical models being actively developed in order to explain the disk formation process in the delta Sco system and Be stars in general.