Is there a problem in ZPP not yet in P?
The Problem:

Input: $\;\;$ a tuple that parses as $\:\langle \hspace{.04 in}p,\hspace{-0.03 in}y,\hspace{-0.03 in}i\hspace{.02 in}\rangle$

Output:

if $p$ is prime and $y$ is a quadratic residue modulo $p$, $\;$ then the $\hspace{.02 in}i\hspace{.03 in}$th$\hspace{.01 in}$ bit of the

non-negative integer $x$ that satisfies $\;\;\; x^{\hspace{.02 in}2} \equiv y \; \pmod p\;\;\;$ and $\;\; 2\hspace{-0.04 in}\cdot \hspace{-0.04 in}x \: \leq \: p \;\;$,

else 0



According to the wiki article, that problem is in ZPP but is not known to be in P.