As part of a project devoted to the phytochemical study of Ecuadorian biodiversity, new essential oils are systematically distilled and analysed. In the present work, Jungia rugosa Less (Asteraceae) has been selected and some wild specimens collected to investigate the volatile fraction. The essential oil, obtained from fresh leaves, was analysed for the first time in the present study. The chemical composition was determined by gas chromatography, coupled to mass spectrometry (GC-MS) for qualitative analysis, and to flame ionization detector (GC-FID) for quantitation. The calculation of relative response factors (RRF), based on combustion enthalpy, was carried out for each quantified component. Fifty-six compounds were identified and quantified in a 5% phenyl-polydimethylsiloxane non-polar column and 53 compounds in a polyethylene glycol polar column, including four undetermined compounds. The main feature of this essential oil was the exclusive sesquiterpenes content, both hydrocarbons (74.7% and 80.4%) and oxygenated (8.3% and 9.6%). Major constituents were: γ-curcumene (47.1% and 49.7%) and β-sesquiphellandrene (17.0% and 17.9%), together with two abundant undetermined oxygenated sesquiterpenes, whose abundance was 6.7–7.2% and 4.7–3.3%, respectively. In addition, the essential oil was submitted to enantioselective evaluation in two β-cyclodextrin-based enantioselective columns, determining the enantiomeric purity of a minor component (1S,2R,6R,7R,8R)-(+)-α-copaene. Finally, the AChE inhibition activity of the EO was evaluated in vitro. In conclusion, this volatile fraction is suitable for further investigation, according to two main lines: (a) the purification and structure elucidation of the major undetermined compounds, (b) a bio-guided fractionation, intended to investigate the presence of new sesquiterpene AChE inhibitors among the minor components.