Octopus laqueus is a small tropical octopus found in Okinawa, Japan and the greater Indo-Pacific. Octopus are often viewed as solitary animals but O. laqueus live in close proximity in the wild, and will potentially encounter one another on a regular basis, raising the possibility of social tolerance. Adopting shared den occupancy in aquaria as a potential measure of social tolerance in O. laqueus, we studied the animals' preference for shared dens over solitude. We characterized dependence of sharing preference on sex, den availability and den occupancy density. We designed two simple social tolerance assays in aquaria with a total of 45 daily measurements: (i) Pots Equal, with equal numbers of octopuses and dens and (ii) Pots Limited, with a 3:1 ratio of octopuses to dens. We found that O. laqueus will socially tolerate other individuals by sharing tanks and dens and with typically no loss to cannibalism or escape. However, animals also exhibit significant levels of social repulsion, and individuals often chose a solitary den when given the option. The patterns of den occupancy are observed to be consistent with a maximum entropy model that balances seeking shelter against avoiding other animals. The model accurately captures and predicts the data and can be generalized to other organisms and their social interactions. Overall, in O. laqueus the preference for a den is stronger than the preference to be solitary. The animals are tolerant of others with a mixture of sizes in the tank and even in a den, a reported first for octopuses outside mating. The relaxed disposition and social tolerance of O. laqueus make it a promising species to work with in the lab to explore social and potentially other behaviors in octopuses.