We present global VLBI observations of the \sim 8100 km s ^ { -1 } H I absorption feature detected toward the strong radio nucleus 3C 84 of NGC 1275 in the Perseus cluster ( { V _ { sys } \sim } 5200 km s ^ { -1 } ) . The observations were obtained using the Very Long Baseline Array ( VLBA ) , the phased Very Large Array ( VLA ) , and three stations of the European VLBI Network ( EVN ) . Our results provide the first high dynamic range image of this feature at high spectral and spatial resolutions . We detect six distinct absorption peaks with optical depths ranging from 0.1 to 0.45 , and multiple weak features with \tau \leq 0.1 . The compactness of the background radio source 3C 84 , which has a linear extent of only about 16 pc , limits the conclusions that can be drawn as to the nature of the intervening object , which must be falling toward the center of the Perseus cluster at \sim 3000 km s ^ { -1 } . However , the detected absorption peaks indicate the existence of several H I clouds with velocity differences and widths similar to those seen in Galactic neutral hydrogen absorption and similar to some of the H I absorption seen in the Large Magellanic Cloud . The most prominent H I clouds extend from 12 to 30 mas ( milliarcseconds ) on the plane of the sky . The derived H I column densities , assuming T _ { s } = 50 K , range over ( 0.35 - 3.8 ) \times 10 ^ { 20 } cm ^ { -2 } , and the implied volume densities range between 1.4 and 11 cm ^ { -3 } .