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Let $Gamma=PSL(2,Z[i])$ be the Picard group and $H^3$ be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient $Gamma setminus H^3$, called the Picard manifold, obtaining an error term of size $O(X^{3/2+theta/2+epsilon})$, where $theta$ denotes a subconvexity exponent for quadratic Dirichlet $L$-functions defined over Gaussian integers.
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