  Asymmetric lemon billiards was introduced in [CMZZ], where the billiard table
$Q(r,b,R)$ is the intersection of two round disks with radii $r\le R$,
respectively, and $b$ measures the distance between the two centers. It is
conjectured [BZZ] that the asymmetric lemon billiards is hyperbolic when the
arc $\Gamma_r$ is a major arc and $R$ is large. In this paper we prove this
conjecture for sufficiently large $R$.
