We construct a total Boolean function $f$ satisfying
$R(f)=\tilde{\Omega}(Q(f)^{5/2})$, refuting the long-standing
conjecture that $R(f)=O(Q(f)^2)$ for all total Boolean functions.
Assuming a conjecture of Aaronson and Ambainis about optimal quantum speedups for partial functions,
we improve this to $R(f)=\tilde{\Omega}(Q(f)^3)$.
Our construction is motivated by the Göös-Pitassi-Watson function
but does not use it.