Geoheritage sites are important resources due to the diverse ways in which they can be utilized. There are small, low-ranked geosites that have attracted significant attention from the lay public. This study reports on one such geosite from the Hosta area of the Western Caucasus. Field observations allowed us to make judgments related to its geoheritage properties and establish the factors for its successful touristic exploitation. This geosite represents a furrow in the Upper Cretaceous limestones in the area, which inherited the former weak zone or minor fault and grew due to landslides. The degree of uniqueness of this geosite is low; it is curvilinear in space; it boasts perfect accessibility, including from a nearby resort, and its landscape context is scenic. The Labyrinth geosite is located in a yew–boxwood grove in the natural reserve, and it is visited by crowds of tourists. Three direct factors in its exploitation success are proposed as follows: story (popular explanation of the geosite’s origin), route (inclusion into a popular touristic route through the grove), and cultural appeal (analogy to man-made labyrinths). Applying these factors to another geoheritage-rich area of the Western Caucasus implied that some of them may not be meaningful according to objective reasons, but that there are other important factors such as geoproduct (particularly geofood) selling. It is also noted that the small size and relatively low value of geosites do not necessarily limit their geotouristic potential. Overall, this case study suggests that “selling” geosites successfully requires advanced, innovative solutions and significant creativity.