We studied the effect of substituting partially, cocoa butter (CB) with Sacha Inchi (Plukenetia volubilis L.) oil (SIO) on rheology, bioactive properties, and sensory preferences in potentially functional chocolate. For this 70% dark chocolates were prepared and the CB was substituted with 1.5%, 3%, and 4.5% of SIO. Hardness and viscosity of the SIO-chocolates were significantly reduced compared to the control (5451 ± 658 g; 17.01 ± 0.94 Pa s, respectively). Total phenolic content remained constant while the antioxidant capacity increased up to IC50 of 2.48 ± 0.10 as the content of SIO increased. The Casson yield stress and Casson plastic viscosity decreased as the amount of SIO increased. Chocolates with 4.5% SIO had a similar color, better glossiness, preferable snap attributes, and were more accepted (7.50 ± 0.08) compared to the control (p < 0.05), measured with a hedonic scale. Then, SIO can improve the bioactive properties of dark chocolates obtaining a potentially functional food with acceptable physicochemical characteristics. SIO can be considered as a new cocoa butter equivalent.