Hyperbolic media have attracted much attention in the photonics community, thanks to their ability to confine light to arbitrarily small volumes and to their use for super-resolution applications. The 2D counterpart of these media can be achieved with hyperbolic metasurfaces, which support in-plane hyperbolic guided modes thanks to nanopatterns which, however, pose significant fabrication challenges and limit the achievable confinement. We show that thin flakes of the van der Waals material α-MoO3 can support naturally in-plane hyperbolic polariton guided modes at mid-infrared frequencies without any patterning. This is possible because α-MoO3 is a biaxial hyperbolic crystal, with three different Restrahlen bands, each for a different crystal axis. Our findings can pave the way towards new paradigm to manipulate and confine light in planar photonic devices.