We propose to investigate the highly one-dimensional (1D) S=1/2 Heisenberg antiferromagnet (NO)[Cu(NO3)3] which is a potential realization of the Nersesyan-Tsvelik model. The spin-1/2 Cu2+ ions are coupled into chains by antiferromagnetic interaction J. These chains are then coupled together by two much weaker antiferromagnetic interactions which are potentially frustrated, J¿ and J2. For the special case J>>J¿=2J2 which corresponds to the Nersesyan-Tsvelik model the interchain interactions effectively cancel completely suppressing long-range order and the ground state is predicted to be a resonating valance bond. We plan to investigate the excitation spectrum of (NO)[Cu(NO3)3 at low energies to establish where (NO)[Cu(NO3)3] lies within the J-J¿-J2 (how close to the Nersesyan-Tsvelik point) and to investigate the nature of the excitations.