  We show that for a smooth projective variety $X$ over a field $k$ and a
reduced effective Cartier divisor $D \subset X$, the Chow group of 0-cycles
with modulus $\mathrm{CH}_0(X|D)$ coincides with the Suslin homology $H^S_0(X
\setminus D)$ under some necessary conditions on $k$ and $D$. We derive several
consequences, and we answer to a question of Barbieri-Viale and Kahn.
