In light of the diminishing presence of physical third places -- informal gathering spaces essential for social connection -- this study explores how the social media platform Discord fosters third-place experiences. Drawing on Oldenburg's conceptual framework, we analyze how Discord's design elements support the creation of virtual third places that foster both dyadic and community-based relationships. Through 25 semi-structured interviews with active Discord users, we identified 21 design elements aligned with Oldenburg's third-place characteristics. These elements cluster around four core principles: providing themed spaces for repeated interactions, supporting user autonomy and customization, facilitating mutually engaging activities, and enabling casual, low-pressure interactions. This work contributes to understanding how intentional platform design can cultivate virtual spaces that support meaningful social connections. The findings have implications for designing future social technologies that can help address growing concerns about social isolation in an increasingly digital world.