  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, $\sigma_{V_r}\lesssim1\,\rm km\,s^{-1}$,
is metal-poor, $\rm [Fe/H]\approx-2.3$, with little $\rm [Fe/H]$ spread and
some variation in $\rm [\alpha/Fe]$ 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.
