  We study the deformations of the Chow group of zero-cycles of the special
fibre of a smooth scheme over a henselian discrete valuation ring. Our main
tools are Bloch's formula and differential forms. As a corollary we get an
algebraization theorem for thickened zero-cycles previously obtained using
idelic techniques. In the course of the proof we develop moving lemmata and
Lefschetz theorems for cohomology groups with coefficients in differential
forms.
