Seismic surface wave tomography is a tried and tested method to reveal the subsurface structure of the Earth. However, the conventional 2-step scheme of inverting first for 2-D maps of surface wave phase or group velocity and then inverting for the 3-D spatial velocity structure preserves little information about lateral spatial correlations, and introduces additional uncertainties and errors into the 3-D result. We introduce a 1-step 3-D non-linear surface wave tomography method that removes these effects by inverting for 3-D spatial structure directly from frequency-dependent traveltime measurements. We achieve this using the reversible jump Markov chain Monte Carlo (McMC) algorithm with a fully 3-D model parametrization. Synthetic tests show that the method estimates the velocity model and associated uncertainties significantly better than the conventional 2-step McMC method, and that the computational cost seems to be comparable with 2-step McMC methods. The resulting uncertainties are more intuitively reasonable than those from the 2-step method, and provide directly interpretable uncertainty on volumetrics of structures of interest.