  We present a 6-D map of the Orphan-Chenab (OC) stream by combining the data
from Southern Stellar Stream Spectroscopic Survey ($S^5$) and {\it Gaia}. We
reconstruct the proper motion, radial velocity, distance, on-sky track and
stellar density along the stream with spline models. The stream has a total
luminosity of $M_V=-8.2$ and metallicity of $\mathrm{[Fe/H]}=-1.9$, similar to
classical Milky Way (MW) satellites like Draco. The stream shows drastic
changes in its physical width varying from 200 pc to 1 kpc, but a constant line
of sight velocity dispersion of 5 km/ss. Despite the large apparent variation
in the stellar number density along the stream, the flow rate of stars along
the stream is remarkably constant. We model the 6-D stream track by a
Lagrange-point stripping method with a flexible MW potential in the presence of
a moving extended Large Magellanic Cloud (LMC). This allows us to constrain the
mass profile of the MW within the distance range 15.6 < r < 55.5 kpc, with the
best measured enclosed mass of $(2.85\pm 0.1)\times 10^{11}\,M_\odot$ within
32.4 kpc. Our stream measurements are highly sensitive to the LMC mass profile
with the most precise measurement of its enclosed mass made at 32.8 kpc,
$(7.02\pm 0.9)\times10^{10}\, {\rm M}_\odot$. We also detect that the LMC dark
matter halo extends to at least 53 kpc. The fitting of the OC stream allows us
to constrain the past LMC trajectory and the degree of dynamical friction it
experienced. We demonstrate that the stars in the OC stream show large energy
and angular momentum spreads caused by LMC perturbation.
