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CD-35 2722 B is an L dwarf companion to the nearby, ∼50-200 Myr old M1 dwarf CD-35 2722 A. We present a detailed analysis of both objects using high-resolution (R ∼ 35,000) K-band spectroscopy from the Keck Planet Imager and Characterizer combined with archival photometry. With a mass of $3{0}_{-4}^{+5}\,{M}_{{\rm{Jup}}}$ (planet-to-host mass ratio 0.05) and projected separation of 67 ± 4 au from its host, CD-35 2722 B likely formed via gravitational instability. We explore whether the chemical composition of the system tells a similar story. Accounting for systematic uncertainties, we find $[{\rm{M}}/{\rm{H}}]=-0.{16}_{-0.02}^{+0.03}\,(\mathrm{stat})\pm 0.25\,(\mathrm{sys})$ dex and ${}^{12}{\rm{C}}{/}^{13}{\rm{C}}\,=13{2}_{-14}^{+20}$ for the host, and $[{\rm{M}}/{\rm{H}}]=0.{27}_{\mathrm{-0.06}}^{\mathrm{+0.07}}\,(\mathrm{stat})\mathrm{\pm 0.12}\,(\mathrm{sys})$ dex, ${}^{12}\mathrm{CO}{/}^{13}\mathrm{CO}={159}_{-24}^{+33}\,{(\mathrm{stat})}_{-33}^{+40}\,(\mathrm{sys})$, and C/O = 0.55 ± 0.01 (stat) ± 0.04 (sys) for the companion. The chemical compositions for the brown dwarf and host star agree within the 1.5σ level, supporting a scenario where CD-35 2722 B formed via gravitational instability. We do not find evidence for clouds on CD-35 2722 B despite it being a photometrically red mid-L dwarf and thus expected to be quite cloudy. We retrieve a temperature structure that is more isothermal than models and investigate its impact on our measurements, finding that constraining the temperature structure to self-consistent models does not significantly impact our retrieved chemical properties. Our observations highlight the need for data from complementary wavelength ranges to verify the presence of aerosols in likely cloudy L dwarfs.