  We investigate signatures induced by a very light pseudoscalar Higgs in
neutralino decays in the Next-to-Minimal Supersymmetric Standard Model (NMSSM)
and determine their observability at the LHC. We concentrate on scenarios which
feature two light scalar Higgs bosons (one of them is SM-like with a mass of
125 GeV and a singlet-like lighter one) with a very light (singlet-like)
pseudoscalar Higgs in the mass range 2m_tau < m_a1 < 2m_b. We consider
neutralino-chargino pair production and the subsequent decay X_{2,3}-> X_1 a1,
which leads to topologies involving multi-leptons and missing transverse
energy. We determine a set of selection cuts that can effectively isolate the
signal from backgrounds of the Standard Model or the Minimal Supersymmetric
Standard Model. We also exemplify the procedure with a set of benchmark points,
for which we compute the expected number of events and signal strength for LHC
with 8 TeV center of mass energy. We show that this signal can already be
probed for some points in the NMSSM parameter space.
