  We present the first direct ejecta velocity measurements of Tycho's supernova
remnant (SNR). Chandra's high angular resolution images reveal a patchy
structure of radial velocities in the ejecta that can be separated into
distinct redshifted, blueshifted, and low velocity ejecta clumps or blobs. The
typical velocities of the redshifted and blueshifted blobs are <~ 7,800 km/s
and <~ 5,000 km/s, respectively. The highest velocity blobs are located near
the center, while the low velocity ones appear near the edge as expected for a
generally spherical expansion. Systematic uncertainty on the velocity
measurements from gain calibration was assessed by carrying out joint fits of
individual blobs with both the ACIS-I and ACIS-S detectors. We determine the
three-dimensional kinematics of the Si- and Fe-rich clumps in the southeastern
quadrant and show that these knots form a distinct, compact, and
kinematically-connected structure, possibly even a chain of knots strung along
the remnant's edge. By examining the viewing geometries we conclude that the
knots in the southeastern region are unlikely to be responsible for the high
velocity Ca II absorption features seen in the light echo spectrum of SN 1572,
the originating event for Tycho's SNR.
