  In an ongoing search for low-mass extreme emission line galaxies, we
identified a galaxy with a Ha/Hb Balmer line ratio of 2.620 +- 0.078. Ha/Hb
Balmer ratios lower than the dust-free Case~B value appear relatively
frequently in extreme emission line galaxies. These low values suggest that the
Case~B assumption may not be valid in these objects. After ruling out the
possibility that the low Ha/Hb ratio is due to systematic errors introduced by
observational effects, we use constraints from the total Hb luminosity, the
[OIII]/[OII] line ratio and the Balmer line equivalent widths, to suggest that
the gas is optically thick to both Ha and Lya photons, and the geometry and
orientation of the scattering gas causes Ha photons to be preferentially
removed from the line of sight with respect to higher order Balmer series
photons. Finally, we use data from the SDSS survey to show that Balmer
self-absorption may be more important than previously assumed in high
excitation emission line galaxies, where Lya pumping of the hydrogen excited
state can be effective. If not recognized, Balmer self-absorption could lead to
inaccurate estimates of galaxy physical properties. As an example, the effect
of dust extinction could be over-estimated, for spherically symmetric
scattering medium, or under-estimated, for a not spherically-symmetric
distribution.
