An approximate treatment of the rotation-vibration interaction is considered in the helium trimer system to study the existence of bound states with non-zero (J = 1) total angular momentum and to elucidate its Efimov character. With the interaction used here, at least one bound state is found. In terms of a lambda -parameter modifying the strength of the two-body potential, the radial part of the wave function changes dramatically with tiny variations around the physical value lambda = 1. High-resolution rotational Raman spectroscopy in a supersonic beam expansion is proposed as a feasible way of observing the bound state predicted.