  We introduce a bosonic ambitwistor string theory in AdS space. Even though
the theory is anomalous at the quantum level, one can nevertheless use it in
the classical limit to derive a novel formula for correlation functions of
boundary CFT operators in arbitrary space-time dimensions. The resulting
construction can be treated as a natural extension of the CHY formalism for the
flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as
integrals over the moduli space of Riemann spheres with punctures. These
integrals localize on an operator-valued version of scattering equations, which
we derive directly from the ambitwistor string action on a coset manifold. As a
testing ground for this formalism we focus on the simplest case of ambitwistor
string coupled to two current algebras, which gives bi-adjoint scalar
correlators in AdS. In order to evaluate them directly, we make use of a series
of contour deformations on the moduli space of punctured Riemann spheres and
check that the result agrees with tree level Witten diagram computations to all
multiplicity. We also initiate the study of eigenfunctions of scattering
equations in AdS, which interpolate between conformal partial waves in
different OPE channels, and point out a connection to an elliptic deformation
of the Calogero-Sutherland model.
