Let $F:M\to M$ be a $C^r$ diffeomorphism, $r\ge 1$, of a smooth surface. If $p$ is a hyperbolic saddle fixed point and $W^s(p)$ intersects $W^u(p)$ transversely at a homoclinic point $q\ne p$, then some iterate $F^N$ has a horseshoe on a compact invariant set near the homoclinic tangle. In particular, $F$ has a compact invariant set on which an iterate is conjugate to a full shift on finitely many symbols.