Details:

Definition: A class $\mathcal{G}$ of groups satisfies the Tits alternative if for any $G$ in $\mathcal{G}$ either $G$ has a free, non-abelian subgroup or $G$ has a solvable subgroup of finite index.

The Request:

I need a reference, please, for the theorem that hyperbolic groups satisfy the Tits Alternative.

(Please see the Wikipedia article linked to above for a definition of hyperbolic groups.)