  Let $k$ be the function field of a complex curve or the field $C((t))$. We
show that for a smooth complete intersection $X$ of $r$ hypersurfaces in
$P^n_k$ of respective degrees $d_1,...,d_r$ with $\sum d_i^2\leq n+1$ the
R-equivalence on rational points of $X$ is trivial and the Chow group of
zero-cycles of degree zero $A_0(X)$ is zero.
