The local interstellar medium (LISM) is made of 15 separate clouds in a region of space around our solar system that extends 15 pc around us. It is composed of gas and dust, and interacts with our Sun as it traverses space, producing the heliosphere. We have been using the growing sample of high resolution UV spectra of nearby stars, obtained by the Hubble Space Telescope (HST), to understand the physical properties and morphology of the LISM. By using HST’s Space Telescope Imaging Spectrograph, we studied one particular sightline 35.8 pc away that had previously been studied for LISM absorption of Mg II (Konow et al. 2020) and Hydrogen’s Lyman-alpha line (Wood et al. 2018). This sightline, a binary star named EK Draconis (HD129333), reveals deuterium (D I) absorption associated with the Local Interstellar Cloud, the structure that directly surrounds our solar system. We used a simultaneous fit to incorporate the D I doublet at 1215.3430 Å and 1215.3376 Å and compared it directly to the Mg II fit, H Ly-α line fit, and the average values for the LISM. We find the D I column density to be comparable to the weighted mean of that throughout the LISM, and the Doppler parameter to be slightly lower, indicating that it is probing a slightly cooler and less turbulent region than the average LISM cloud. Finally, the velocity of the D I gas at EK Dra is unexpectedly blueshifted from the velocity found for Mg II and H I of the same sight line. We explore possible explanations and compare these findings. A global fit of the entire Lyman-α profile, with D I and H I interstellar absorption and possible contributions of heliospheric or astrospheric absorption, provides a more robust determination of the LISM parameters. Deuterium is an isotope of hydrogen that is valuable for modeling and comparison to the optically thick hydrogen Lyman-α, enabling direct measurements of our heliosphere, the ISM, and the astrosphere around the host star. We gratefully acknowledge the National Science Foundation’s support of the Keck Northeast Astronomy Consortium’s REU program through grant AST-1950797.