Abstract: I will describe an extension of a theorem of R. Coifman and Y. Meyer regarding bilinear pseudo-differential operators to bilinear Fourier integral operators. More precisely, we prove the global $L^2 times L^2 to L^1$ boundedness of bilinear Fourier integral operators with amplitudes in the class $S^0_{1,0}$. The proof makes use of a quadratic $T(1)$-theorem and commutator estimates. This is joint work with Wolfgang Staubach and Salvador Rodriguez-Lopez.