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The $100^\circ$-long thin stellar stream in the Milky Way halo, GD-1, has an ensemble of features that may be due to dynamical interactions. Using high-resolution MMT/Hectochelle spectroscopy we show that a spur of GD-1-like stars outside of the main stream are kinematically and chemically consistent with the main stream. In the spur, as in the main stream, GD-1 has a low intrinsic radial velocity dispersion, $σ_{V_r}\lesssim1\,\rm km\,s^{-1}$, is metal-poor, $\rm [Fe/H]\approx-2.3$, with little $\rm [Fe/H]$ spread and some variation in $\rm [α/Fe]$ abundances, which point to a common globular cluster progenitor. At a fixed location along the stream, the median radial velocity offset between the spur and the main stream is smaller than $0.5\,\rm km\,s^{-1}$, comparable to the measurement uncertainty. A flyby of a massive, compact object can change orbits of stars in a stellar stream and produce features like the spur observed in GD-1. In this scenario, the radial velocity of the GD-1 spur relative to the stream constrains the orbit of the perturber and its current on-sky position to $\approx5,000\,\rm deg^2$. The family of acceptable perturber orbits overlaps the stellar and dark-matter debris of the Sagittarius dwarf galaxy in present-day position and velocity. This suggests that GD-1 may have been perturbed by a globular cluster or an extremely compact dark-matter subhalo formerly associated with Sagittarius.