  The decay K_L -> pi0 e+ e- is being searched for as a signal of direct Delta
S = 1 CP violation. We provide a thorough updating of the analysis of the three
components of the decay: 1) Direct CP violation, 2) CP violation through the
mass matrix and 3) CP-conserving (two-photon) contributions. First the chiral
calculation of the K_S -> pi0 e+ e- rate, due to Ecker, Pich and de Rafael
(EPR), is updated to include recent results on the nonleptonic amplitude. Then
we systematically explore the uncertainties in this method. These appear to be
so large that they will obscure the direct CP violation unless it is possible
to measure the K_S -> pi0 e+ e- rate. The CP-conserving amplitude remains
somewhat uncertain, but present indications are such that there may be a
sizable CP-violating asymmetry in the e+, e- energies from the interference of
the CP-conserving and CP-violating amplitudes and this may potentially be
useful in determining whether direct CP violation is present.
