  While protoplanetary disks often appear to be compact and well-organized in
millimeter continuum emission, CO spectral line observations are increasingly
revealing complex behavior at large distances from the host star. We present
deep ALMA maps of the $J=2-1$ transition of $^{12}$CO, $^{13}$CO, and
C$^{18}$O, as well as the $J=3-2$ transition of DCO$^+$, toward the T Tauri
star RU Lup at a resolution of $\sim0.3''$ ($\sim50$ au). The CO isotopologue
emission traces four major components of the RU Lup system: a compact Keplerian
disk with a radius of $\sim120$ au, a non-Keplerian ``envelope-like'' structure
surrounding the disk and extending to $\sim260$ au from the star, at least five
blueshifted spiral arms stretching up to 1000 au, and clumps outside the spiral
arms located up to 1500 au in projection from RU Lup. We comment on potential
explanations for RU Lup's peculiar gas morphology, including gravitational
instability, accretion of material onto the disk, or perturbation by another
star. RU Lup's extended non-Keplerian CO emission, elevated stellar accretion
rate, and unusual photometric variability suggest that it could be a
scaled-down Class II analog of the outbursting FU Ori systems.
