  We consider a homogeneous 1D Bose gas with contact interactions and large
attractive coupling constant. This system can be realized in tight waveguides
by exploiting a confinement induced resonance of the effective 1D scattering
amplitude. By using a variational {\it ansatz} for the many-body wavefunction,
we show that for small densities the gas-like state is stable and the
corresponding equation of state is well described by a gas of hard rods. By
calculating the compressibility of the system, we provide an estimate of the
critical density at which the gas-like state becomes unstable against cluster
formation. Within the hard-rod model we calculate the one-body density matrix
and the static structure factor of the gas. The results show that in this
regime the system is more strongly correlated than a Tonks-Girardeau gas. The
frequency of the lowest breathing mode for harmonically trapped systems is also
discussed as a function of the interaction strength.
