The Ophiuchus stream is a recently discovered stellar tidal stream in the Milky Way. We present high-quality spectroscopic data for 14 stream member stars obtained using the Keck and MMT telescopes. We confirm the stream as a fast moving ($v_{los}sim290$ km s$^{-1}$), kinematically cold group ($sigma_{v_{los}}lesssim1$ km s$^{-1}$) of $alpha$-enhanced and metal-poor stars (${rm [alpha/Fe]sim0.4}$ dex, ${rm [Fe/H]sim-2.0}$ dex). Using a probabilistic technique, we model the stream simultaneously in line-of-sight velocity, color-magnitude, coordinate, and proper motion space, and so determine its distribution in 6D phase-space. We find that that the stream extends in distance from 7.5 to 9 kpc from the Sun; it is 50 times longer than wide, merely appearing highly foreshortened in projection. The analysis of the stellar population contained in the stream suggests that it is $sim12$ Gyr old, and that its initial stellar mass was $sim2times10^4$ $M_{odot}$ (or at least $gtrsim7times10^3$ $M_{odot}$). Assuming a fiducial Milky Way potential, we fit an orbit to the stream which matches the observed phase-space distribution, except for some tension in the proper motions: the stream has an orbital period of $sim350$ Myr, and is on a fairly eccentric orbit ($esim0.66$) with a pericenter of $sim3.5$ kpc and an apocenter of $sim17$ kpc. The phase-space structure and stellar population of the stream show that its progenitor must have been a globular cluster that was disrupted only $sim240$ Myr ago. We do not detect any significant overdensity of stars along the stream that would indicate the presence of a progenitor, and conclude that the stream is all that is left of the progenitor.
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