  Let $D > 546$ be the discriminant of an indefinite rational quaternion
algebra. We show that there are infinitely many imaginary quadratic fields
$l/\mathbb Q$ such that the twist of the Shimura curve $X^D$ by the main
Atkin-Lehner involution $w_D$ and $l/\mathbb Q$ violates the Hasse Principle
over $\mathbb Q$.
