The simplest supersymmetric model that solves the μ problem and in which the GUT-scale parameters need not be finely tuned in order to predict the correct value of the Z boson mass at low scales is the Next-to-Minimal Supersymmetric Standard Model (NMSSM). However, in order that fine tuning be absent, the lightest CP-even Higgs boson h should have mass ∼ 100 GeV and SM couplings to gauge bosons and fermions. The only way that this can be consistent with LEP limits is if h decays primarily via h aa τ +τ -τ +τ - or 4j but not 4b, where a is the lighter of the two pseudo-scalar Higgses that are present in the NMSSM. Interestingly, m a <2m b is natural in the NMSSM with m a > 2m τ somewhat preferred. Thus, h τ +τ -τ +τ - becomes a key mode of interest. Meanwhile, all other Higgs bosons of the NMSSM are typically quite heavy. Detection of any of the NMSSM Higgs bosons at the LHC in this preferred scenario will be very challenging using conventional channels. In this paper, we demonstrate that the h aa τ +τ -τ +τ - decay chain should be visible if the Higgs is produced in the process pp p+h+p with the final state protons being measured using suitably installed forward detectors. Moreover, we show that the mass of both the h and the a can be determined on an event-by-event basis.