We have assembled a collection of PKP data from broadband records of the Geoscope network. This collection is unique because, for the first tie, it includes polar paths at epicentral distances between 172¿ and 177¿, for which PKPDF samples the central part of the inner core. After Hilbert transforming the DF branch, the waveforms of PKPAB and PKPDF usually become very similar, and we measure differential travel times with an accuracy of a fraction of a second. The differential (AB-DF) times for equatorial paths are close to those predicted by PREM, whereas for the polar paths, they are larger by 3 to 6 sec. Absolute DF times confirm that the effect is primarily in the inner core. These observations are compatible with a model of cylindrical anisotropy in the inner core with the axis of symmetry aligned with the Earth's spin axis and an amplitude of 3.5%. They require that the anisotropy extend to the central part of the inner core, confirming extrapolations made by Creager (1992) and ruling out models where anisotropy is confined to the outer 300 km of the inner core (Tromp, 1993). ¿ American Geophysical Union 1994