We present new Hubble Space Telescope - Cosmic Origins Spectrograph ( HST-COS ) G130M spectroscopy which we have obtained for a sightline toward a filament projected 1.9 kpc from the nucleus of M87 , near the edge of the inner radio lobe to the east of the nucleus . The combination of the sensitivity of COS and the proximity of M87 allows us to study the structure of this filament in unparalleled detail . We propose that the filament is composed of many cold clumps , each surrounded by an FUV-emitting boundary layer , with the filament having a radius r _ { c } \sim 10 pc and the clumps filling the cylinder with a low volume filling factor . The observed velocity dispersion in emission lines from the filament results from the random motions of these clumps within the filament . We measure fluxes and kinematics for emission lines of Ly \alpha , C ii \lambda 1335 , and N v \lambda 1238 , finding v _ { r } = 147 \pm 2 km s ^ { -1 } , 138 \pm 18 km s ^ { -1 } , and 148 ^ { +14 } _ { -16 } km s ^ { -1 } relative to M87 , and line broadenings \sigma _ { r } = 171 \pm 2 km s ^ { -1 } , 189 ^ { +12 } _ { -11 } km s ^ { -1 } , and 128 ^ { +23 } _ { -17 } km s ^ { -1 } respectively . We associate these three lines , as well as archival measurements of H \alpha , C iv \lambda 1549 , and He ii \lambda 1640 , with a multitemperature boundary layer around clumps which are moving with supersonic random motions in the filament . This boundary layer is a significant coolant of the hot gas . We show that the [ C ii ] \lambda 158 \mu m flux observed by Herschel-PACS from this region implies the existence of a massive cold ( T \sim 10 ^ { 3 } K ) component in the filament which contains significantly more mass ( M \sim 8000 M _ { \odot } within our r \approx 100 pc sightline ) than the FUV-emitting boundary layer . It has about the same bulk velocity and velocity dispersion as the boundary layer . We also detect [ Fe xxi ] \lambda 1354 in emission at 4 - 5 \sigma . This line is emitted from 1 keV ( T \approx 10 ^ { 7 } K ) plasma , and we use it to measure the bulk radial velocity ( v _ { r } = -92 ^ { +34 } _ { -22 } km s ^ { -1 } ) and velocity dispersion ( \sigma _ { r } = 69 ^ { +79 } _ { -27 } km s ^ { -1 } ) of the plasma at this temperature . In contrast to the intermediate-temperature FUV lines , [ Fe xxi ] is blueshifted relative to M87 and matches the bulk velocity of a nearby filament to the south . We hypothesize that this line arises from the approaching face of the radio bubble expanding through this sightline , while the filament lies on the receding side of the bubble . A byproduct of our observations is the detection of absorption from interstellar gas in our Galaxy , observed in C ii \lambda 1335 and Ly \alpha .