The present study describes the chemical and enantiomeric composition of a new essential oil, distilled from the dry leaves of Gynoxys buxifolia (Kunth) Cass. The chemical analysis was conducted by GC-MS and GC-FID, on two orthogonal capillary columns. A total of 72 compounds were detected and quantified with at least one column, corresponding to about 85% by weight of the whole oil mass. Of the 72 components, 70 were identified by comparing the respective linear retention indices and mass spectra with data from the literature, whereas the two main constituents were identified by preparative purification and NMR experiments. The quantitative analysis was carried out calculating the relative response factor of each compound according to their combustion enthalpy. The major constituents of the EO (≥3%) were: furanoeremophilane (31.3–28.3%), bakkenolide A (17.6–16.3%), caryophyllene oxide (6.0–5.8%), and (E)-β-caryophyllene (4.4%). Additionally, the hydrolate was also analyzed with respect to the dissolved organic phase. About 40.7–43.4 mg/100 mL of organic compounds was detected in solution, of which p-vinylguaiacol was the main component (25.4–29.9 mg/100 mL). Finally, the enantioselective analysis of some chiral terpenes was carried out, with a capillary column based on β-cyclodextrin chiral stationary phase. In this analysis, (1S,5S)-(−)-α-pinene, (1S,5S)-(−)-β-pinene, (S)-(+)-α-phellandrene, (S)-(+)-β-phellandrene, and (S)-(−)-terpinen-4-ol were detected as enantiomerically pure, whereas (S)-(−)-sabinene showed an enantiomeric excess of 69.2%. The essential oil described in the present study is a good source of two uncommon volatile compounds: furanoeremophilane and bakkenolide A. The former lacks bioactivity information and deserves further investigation, whereas the latter is a promising selective anticancer product.