Pilots operating aircraft in un-towered airspace rely on their situational awareness and prior knowledge to predict the future trajectories of other agents. These predictions are conditioned on the past trajectories of other agents, agent-agent social interactions and environmental context such as airport location and weather. This paper provides a dataset, $\textit{TrajAir}$TrajAir, that captures this behaviour in a non-towered terminal airspace around a regional airport. We also present a baseline socially-aware trajectory prediction algorithm, $\textit{TrajAirNet}$TrajAirNet, that uses the dataset to predict the trajectories of all agents. The dataset is collected for 111 days over 8 months and contains ADS-B transponder data along with the corresponding METAR weather data. The data is processed to be used as a benchmark with other publicly available social navigation datasets. To the best of authors' knowledge, this is the first 3D social aerial navigation dataset thus introducing social navigation for autonomous aviation. $\textit{TrajAirNet}$TrajAirNet combines state-of-the-art modules in social navigation to provide predictions in a static environment with a dynamic context. Both the $\textit{TrajAir}$TrajAir dataset and $\textit{TrajAirNet}$TrajAirNet prediction algorithm are open-source. The dataset, codebase, and video are available at https://theairlab.org/trajair/, https://github.com/castacks/trajairnet, and https://youtu.be/elAQXrxB2gw respectively.