  In this paper we construct an almost negatively $\frac{1}{4}$-pinched
Riemannian metric on a class of compact manifolds that, via previous work, was
already known to be K\"{a}hler and not locally symmetric. This is the first
known example of such manifolds and, via the result of Hernandez [7] and Yau
and Zheng [14], these manifolds cannot admit a negatively quarter-pinched
Riemannian metric. This metric is also interesting because it is the complex
hyperbolic analogue to the famous pinched metric constructed by Gromov and
Thurston in [6].
