  In the CP-violating Minimal Supersymmetric Standard Model (MSSM), for certain
values of the CP-violating phases associated to the universal trilinear
couplings $(A_t, A_b)$ and the gluino mass $(M_{\tilde g})$, e.g.,
$\Phi_{\rm{CP}} = 60^\circ$ or $90^\circ$, for $M_{H^+} \lsim 140 $ GeV and
$\tan \beta \sim 2-5 $, the lightest Higgs boson mass ($M_{H_1}$) is $\lsim 50
$ GeV. This mass interval is still allowed from standard LEP Higgs searches
because of a strongly suppressed $H_1ZZ$ coupling. However, in the same region
of parameter space in which these two conditions occur, the $H_1 H^\mp W^\pm $
coupling is enhanced because the two mentioned sets of couplings satisfy a sum
rule. In this paper we probe such a light Higgs scenario at the Large Hadron
Collider (LHC) by studying $H^\pm H_1$ associate production, leading to a $4b +
\ell^\pm + \mET $ signal. We show that the latter is readily accessible at the
CERN hadron collider, upon the application of suitable selection cuts against
the Standard Model (SM) backgrounds. Our parton level Monte Carlo (MC) analysis
yields $\sim 15-45 $ signal events, completely free of SM background, for
${\cal L} = 10-30 {\rm fb}^{-1}$ of accumulated luminosity, after taking into
account the overall efficiency for tagging four $b$-jets.
