  We propose an experimental test of a scenario in the Next-to-Minimal
Supersymmetric Standard Model in which both the lightest scalar and the
lightest pseudoscalar Higgs bosons have masses around 125 GeV. The pseudoscalar
can contribute significantly to the gamma.gamma rate at the LHC due to light
Higgsino-like charginos in its effective one-loop coupling to two photons. Such
charginos are obtained for small values of the mu_eff parameter which also
results in enhanced b.b-bar and tau+.tau- rates compared to those expected for
a Standard Model Higgs boson. This scenario should result in a clear
discrepancy between the observed rates in these three decay channels and those
in the WW and ZZ channels, since the pseudoscalar does not couple to the W and
Z bosons. However, in the dominant gluon fusion production mode the
pseudoscalar will stay hidden behind the SM-like scalar Higgs boson and in
order for it to be observable the associated b.b-bar.h production mode has to
be considered, the cross section for which is tiny in the Standard Model but
tan.beta-enhanced in supersymmetry. We analyze the constrained NMSSM with
non-universal Higgs sector parameters and identify regions of its parameter
space where the lightest pseudoscalar with mass around 125 GeV and strongly
enhanced gamma.gamma (up to 60%), b.b-bar and tau+.tau- rates in the b.b-bar.h
mode can be obtained.
