  We study the structure constants of the ${\cal N}=1$ beta deformed theory
perturbatively and at strong coupling. We show that the planar one loop
corrections to the structure constants of single trace gauge invariant
operators in the scalar sector is determined by the anomalous dimension
Hamiltonian. This result implies that 3 point functions of the chiral primaries
of the theory do not receive corrections at one loop. We then study the
structure constants at strong coupling using the Lunin-Maldacena geometry. We
explicitly construct the supergravity mode dual to the chiral primary with
three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3
point function of this supergravity mode with semi-classical states
representing two other similar chiral primary states but with large U(1)
charges to be independent of the beta deformation and identical to that found
in the $AdS_5\times S^5$ geometry. This together with the one-loop result
indicate that these structure constants are protected by a non-renormalization
theorem. We also show that three point function of U(1) R-currents with
classical massive strings is proportional to the R-charge carried by the string
solution. This is in accordance with the prediction of the R-symmetry Ward
identity.
