Burmese amber preserves a diverse assemblage of Cretaceous arachnids, and among pseudoscorpions (Arachnida: Pseudoscorpiones), ten species in five families have already been named. Here, we describe a new fossil species from Burmese amber in the pseudoscorpion family Hyidae, providing detailed measurements, photographs and 3D-models from synchrotron scanning. Based on morphology, the new fossil, Hya fynni sp. nov. is placed in the genus Hya, and is nearly identical to extant species in the genus, except for the position of trichobothrium est on the pedipalpal chela, thereby indicating extreme morphological stasis in this invertebrate lineage over the last 99 million years. Hya fynni represents the first described fossil species in Hyidae, and the third described Burmese fossil in the superfamily Neobisioidea. It also joins the garypinid, Amblyolpium burmiticum, in representing the oldest fossil records for extant pseudoscorpion genera. Considering proposed divergence dates, the newly described fossil species bolsters a Gondwanan origin for Hyidae, and provides evidence for the "Late Jurassic Rifting" hypothesis for the Burma Terrane, in which this landmass rifted from Gondwana in the Late Jurassic and collided with Eurasia by the Cretaceous/Eocene. Like Hya species today, H. fynni likely inhabited humicolous microhabitats in tropical forests on the Burma Terrane, supporting ecological niche stasis for this family since the Mesozoic.