Transient coaxial helicity injection (CHI) in the National Spherical Torus Experiment (NSTX) has generated toroidal current on closed-flux surfaces without the use of the central solenoid. When induction from the central solenoid was added, CHI initiated discharges in NSTX achieved 1 MA of plasma current using 65% of the solenoid flux of standard induction-only discharges. In addition, the CHI-initiated discharges have lower density and a low normalized internal plasma inductance of 0.35, as desired for achieving advanced scenarios. Transient CHI will be used for non-inductive plasma start-up on the upgrade to NSTX (NSTX-U) that is now under construction. It will have numerous improvements that significantly enhance CHI start-up capability. The TSC code is now starting to be used for full discharge simulation, which includes solenoid-less start-up with CHI and subsequent non-inductive current ramp-up using neutral beams. These results suggest that the increased injector flux capability of NSTX-U should allow CHI start-up at more than the 400 kA level and that the new tangential neutral beam system on NSTX-U should be able to ramp the current to the 1 MA levels.