© 2018. The American Astronomical Society. All rights reserved. Calcium-rich gap transients represent an intriguing new class of faint and fast-evolving supernovae that exhibit strong [Ca ii] emission in their nebular phase spectra. In this paper, we present the discovery and follow-up observations of a faint and fast-evolving transient, iPTF 16hgs, that exhibited a double-peaked light curve. Exhibiting a Type Ib spectrum in the photospheric phase and an early transition to a [Ca ii] dominated nebular phase, iPTF 16hgs shows properties consistent with the class of Ca-rich gap transients, with two important exceptions. First, while the second peak of the light curve is similar to other Ca-rich gap transients, the first blue and fast-fading peak (declining over ≈2 days) is unique to this source. Second, we find that iPTF 16hgs occurred in the outskirts (projected offset of ≈6 kpc ≈ 1.9 R eff) of a low-metallicity (≈0.4 Z o), star-forming, dwarf spiral galaxy. Deep limits from late-time radio observations suggest a low-density environment for the source. If iPTF 16hgs shares explosion physics with the class of Ca-rich gap transients, the first peak can be explained by the presence of 0.01 M o of 56Ni in the outer layers the ejecta, reminiscent of some models of He-shell detonations on WDs. However, if iPTF 16hgs is physically unrelated to the class, the first peak is consistent with shock cooling emission (of an envelope with a mass of ≈0.08 M o and radius of ≈13 R o) in a core-collapse explosion of a highly stripped massive star in a close binary system.