Hyperbolic media have attracted much attention in the photonics community due to their ability to confine light to arbitrarily small volumes and their potential applications to super-resolution technologies. The two-dimensional counterparts of these media can be achieved with hyperbolic metasurfaces that support in-plane hyperbolic guided modes upon nanopatterning, which, however, poses notable fabrication challenges and limits the achievable confinement. We show that thin flakes of a van der Waals crystal, α-MoO3, can support naturally in-plane hyperbolic polariton guided modes at mid-infrared frequencies without the need for patterning. This is possible because α-MoO3 is a biaxial hyperbolic crystal with three different Reststrahlen bands, each corresponding to a different crystalline axis. These findings can pave the way toward a new paradigm to manipulate and confine light in planar photonic devices.