  Let E be a modular elliptic curve defined over a rational function field k of
odd characteristic. We construct a sequence of Heegner points on E, defined
over a $Z_p^{\infty}$-tower of finite extensions of k, and show that these
Heegner points generate a group of infinite rank. This is a function field
analogue of a result of C.Cornut and V.Vatsal
