We present an analysis of chandra/LETGS observations of the ultracompact X-ray binary (UCXB) 4U 1626$-$67, continuing our project to analyze the existing Chandra gratings data of this interesting source. The extremely low mass, hydrogen-depleted donor star provides a unique opportunity to study the properties and structure of the metal-rich accreted plasma. There are strong, double-peaked emission features of OVII-VIII and Ne IX-X, but no other identified emission lines are detected. Our spectral fit simultaneously models the emission line profiles and the plasma parameters, using a two-temperature collisionally-ionized plasma. Based on our line profile fitting, we constrain the inclination of the system to 25--60$^{circ}$ and the inner disk radius to $sim$1500 gravitational radii, in turn constraining the donor mass to $lesssim$0.026 M_sun, while our plasma modeling confirms previous reports of high neon abundance in the source, establishing a Ne/O ratio in the system of $0.47 pm 0.04$, while simultaneously estimating a very low Fe/O ratio of $0.0042 pm 0.0008$ and limiting the Mg/O ratio to less than 1% by number. We discuss these results in light of previous work.
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