  The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) is an untargeted
spectroscopic survey that aims to measure the expansion rate of the Universe at
$z \sim 2.4$ to 1% precision for both $H(z)$ and $D_A(z)$. HETDEX is in the
process of mapping in excess of one million Lyman Alpha emitting (LAE) galaxies
and a similar number of lower-z galaxies as a tracer of the large-scale
structure. The success of the measurement is predicated on the post-observation
separation of galaxies with Ly$\alpha$ emission from the lower-$z$ interloping
galaxies, primarily [OII], with low contamination and high recovery rates. The
Emission Line eXplorer (ELiXer) is the principal classification tool for
HETDEX, providing a tunable balance between contamination and completeness as
dictated by science needs. By combining multiple selection criteria, ELiXer
improves upon the 20 Angstrom rest-frame equivalent width cut commonly used to
distinguish LAEs from lower-$z$ [OII] emitting galaxies. Despite a spectral
resolving power, R $\sim800$, that cannot resolve the [OII] doublet, we
demonstrate the ability to distinguish LAEs from foreground galaxies with 98.1%
accuracy. We estimate a contamination rate of Ly$\alpha$ by [OII] of 1.2% and a
Ly$\alpha$ recovery rate of 99.1% using the default ELiXer configuration. These
rates meet the HETDEX science requirements.
