  We present a relation between the classical Chow group of relative $0$-cycles
on a regular scheme $\mathcal{X}$, projective and flat over an excellent
Henselian discrete valuation ring, and the Levine-Weibel Chow group of 0-cycles
on the special fiber. We show that these two Chow groups are isomorphic with
finite coefficients under extra assumptions. This generalizes a result of
Esnault, Kerz and Wittenberg.
