  We calculate the interaction 3-vertex of two massless spin 3 particles with a
graviton using vertex operators for spin 3 fields in open string theory,
constructed in our previous work. The massless spin 3 fields are shown to
interact with the graviton through the linearized Weyl tensor, reproducing the
result by Boulanger, Leclercq and Sundell. This is consistent with the general
structure of the non-Abelian $2-s-s$ couplings, implying that the minimal
number of space-time derivatives in the interaction vertices of two spin s and
one spin 2 particle is equal to $2s-2$.
