  We construct a quadratic curvature theory of gravity whose graviton
propagator around the Minkowski background respects wordline inversion
symmetry, the particle approximation to modular invariance in string theory.
This symmetry automatically yields a corresponding gravitational theory that is
nonlocal, with the action containing infinite order differential operators. As
a consequence, despite being a higher order derivative theory, it is ghost-free
and has no degrees of freedom besides the massless spin-$2$ graviton of
Einstein's general relativity. By working in the linearised regime we show that
the point-like singularities that afflict the (local) Einstein's theory are
smeared out.
