  All curves on a separably rationally connected variety are rationally
equivalent to a (non-effective) integral sum of rational curves, hence the
first Chow group is generated by rational curves. Applying the same techniques,
we also proved that the first Chow group of all separably rationally connected
Fano complete intersections with index at least 2 is generated by lines. As a
consequence, a question of Professor Burt Totaro about integral Hodge classess
on rationally connected 3-folds is solved, and positive answer to the question
for general n-fold due to Professor J\'anos Koll\'ar will follow from the Tate
conjecture for surfaces over finite fields.
