We give new examples of compact, negatively curved Einstein manifolds of dimension
4
4
. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of four-manifolds
(
X
k
)
(X_k)
previously considered by Gromov and Thurston (Pinching constants for hyperbolic manifolds, Invent. Math. 89 (1987), no. 1, 1–12). The construction begins with a certain sequence
(
M
k
)
(M_k)
of hyperbolic four-manifolds, each containing a totally geodesic surface
Σ
k
\Sigma _k
which is nullhomologous and whose normal injectivity radius tends to infinity with
k
k
. For a fixed choice of natural number
l
l
, we consider the
l
l
-fold cover
X
k
→
M
k
X_k \to M_k
branched along
Σ
k
\Sigma _k
. We prove that for any choice of
l
l
and all large enough
k
k
(depending on
l
l
),
X
k
X_k
carries an Einstein metric of negative sectional curvature. The first step in the proof is to find an approximate Einstein metric on
X
k
X_k
, which is done by interpolating between a model Einstein metric near the branch locus and the pull-back of the hyperbolic metric from
M
k
M_k
. The second step in the proof is to perturb this to a genuine solution to Einstein’s equations, by a parameter dependent version of the inverse function theorem. The analysis relies on a delicate bootstrap procedure based on
L
2
L^2
coercivity estimates.