The development and evaluation of Lidar-Inertial Odometry (LIO) and Simultaneous Localization and Mapping (SLAM) systems requires a precise ground truth. The Global Navigation Satellite System (GNSS) is often used as a foundation for this, but its signals can be unreliable in obstructed environments due to multi-path effects or loss-of-signal. While existing datasets compensate for the sporadic loss of GNSS signals by incorporating Inertial Measurement Unit (IMU) measurements, the commonly used Micro-Electro-Mechanical Systems (MEMS) or Fiber Optic Gyroscope (FOG)-based systems do not permit the prolonged study of GNSS-denied environments. To close this gap, we present Odyssey, a LIO dataset with a focus on GNSS-denied environments such as tunnels and parking garages as well as other underrepresented, yet ubiquitous situations such as stop-and-go-traffic, bumpy roads and wide open fields. Our ground truth is derived from a navigation-grade Inertial Navigation System (INS) equipped with a Ring Laser Gyroscope (RLG), offering exceptional bias stability characteristics compared to IMUs used in existing datasets and enabling the prolonged and accurate study of GNSS-denied environments. This makes Odyssey the first publicly available dataset featuring a RLG-based INS. Besides providing data for LIO, we also support other tasks, such as place recognition, through the threefold repetition of all trajectories as well as the integration of external mapping data by providing precise geodetic coordinates. All data, dataloader and other material is available online at https://odyssey.uni-goettingen.de/ .