We present Submillimeter Array observations of the GQ Lup system at 1.3 millimeters wavelength with $0\farcs4$ ($∼$60 AU) resolution. Emission is detected from the position of the primary star, GQ Lup A, and is marginally resolved. No emission is detected from the substellar companion, GQ Lup B, $0\farcs7$ away. These data, together with models of the spectral energy distribution, suggest a compact disk around GQ Lup A with mass $∼ 3$ M$_{Jup}$, perhaps truncated by tidal forces. There is no evidence for a gap or hole in the disk that might be the signature of an additional inner companion body capable of scattering GQ Lup B out to $∼100$ AU separation from GQ Lup A. For GQ Lup B to have formed {\it in situ}, the disk would have to have been much more massive and extended. ; Comment: 16 pages, 2 figures, accepted to AJ