  Effective field theory provides a way of parameterizing strong-field
deviations from General Relativity that might be observable in the
gravitational waves emitted in a black hole merger. To perform numerical
simulations of mergers in such theories it is necessary that the equations be
written in a form that admits a well-posed initial value formulation. We study
gravity coupled to a scalar field including the leading (4-derivative)
effective field theory corrections. We introduce a new class of "modified
harmonic" gauges and gauge-fixed equations of motion, such that, at weak
coupling, the equations are strongly hyperbolic and therefore admit a
well-posed initial value formulation.
