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We present new HST-COS G130M spectroscopy for a sightline toward a filamentprojected 1.9 kpc from the nucleus of M87. The combination of the sensitivityof COS and the proximity of M87 allows us to study the structure of thisfilament in unparalleled detail. We propose that the filament is composed ofmany cold clumps, each surrounded by an FUV-emitting boundary layer, with thefilament having a radius $r_c \sim 10$ pc and the clumps filling the cylinderwith a low volume filling factor. The observed velocity dispersion in emissionlines from the filament results from the random motions of these clumps withinthe filament.  We measure fluxes and kinematics for emission lines of Ly$\alpha$, C II$\lambda$1335, and N V $\lambda1238$. We associate these three lines, as wellas archival measurements of H$\alpha$, C IV $\lambda$1549, and He II$\lambda$1640, with a multitemperature boundary layer around clumps which aremoving with supersonic random motions in the filament. This boundary layer is asignificant coolant of the hot gas. We show that the [C II] $\lambda$158$\mu$mflux observed by Herschel-PACS from this region implies the existence of amassive cold ($T \sim 10^3$ K) component in the filament which containssignificantly more mass than the FUV-emitting boundary layer.  We also detect [Fe XXI] $\lambda$1354 in emission at $4-5\sigma$. This lineis emitted from 1 keV ($T \approx 10^7$ K) plasma, and we use it to measure thebulk radial velocity and velocity dispersion of the plasma at this temperature.In contrast to the intermediate-temperature FUV lines, [\ion{Fe}{xxi}] isblueshifted relative to M87 and matches the bulk velocity of a nearby filamentto the south. We hypothesize that this line arises from the approaching face ofthe radio bubble expanding through this sightline, while the filament lies onthe receding side of the bubble. (abstract is abridged)

FUV line emission, gas kinematics, and discovery of [Fe XXI] $\lambda$1354.1 in the sightline towards a filament in M87