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 strongly coupled by antiferromagnetic interactions J, along the b axis. These chains are then coupled in the bc plane by two much weaker antiferromagnetic interactions which are potentially frustrated, J¿ along c, and J2 in the diagonal b-c direction. 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. Here we plan to investigate the excitation spectrum of (NO)[Cu(NO3)3] and establish where it lies in the J-J¿-J2 phase diagram and whether it is close to the Nersesyan-Tsvelik point.