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 ($v_{los}∼290$ km s$^{-1}$), kinematically cold group ($σ_{v_{los}}\lesssim1$ km s$^{-1}$) of $α$-enhanced and metal-poor stars (${\rm [α/Fe]∼0.4}$ dex, ${\rm [Fe/H]∼-2.0}$ 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 $∼12$ Gyr old, and that its initial stellar mass was $∼2\times10^4$ $M_{⊙}$ (or at least $\gtrsim7\times10^3$ $M_{⊙}$). 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 $∼350$ Myr, and is on a fairly eccentric orbit ($e∼0.66$) with a pericenter of $∼3.5$ kpc and an apocenter of $∼17$ 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 $∼240$ 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. ; Comment: ApJ in press