  The vortex core in chiral p-wave superconductors exhibits various properties
owing to the interplay between the vorticity and chirality inside the vortex
core. In the chiral p-wave superconductors, the site-selective nuclear
spin-lattice relaxation rate T1^{-1} is theoretically studied inside the vortex
core within the framework of the quasiclassical theory of superconductivity.
T1^{-1} at the vortex center depends on the sense of the chirality relative to
the sense of the magnetic field. The effect of a tilt of the magnetic field
upon T1^{-1} is investigated. The effect of the anisotropy in the
superconducting gap and the Fermi surface is then investigated. The result is
expected to be experimentally observed as a sign of the chiral pairing state in
a superconducting material Sr2RuO4.
