High entropy alloys (HEA) are an unusual class of materials where mixtures of elements are stochastically arrayed on a simple crystalline lattice. These systems exhibit remarkable functionality, often along several distinct axes: e.g., the examples [TaNb]1-x(TiZrHf)x are high strength and damage resistant refractory metals that also exhibit superconductivity with large upper critical fields. Here we report the discovery of an f-electron containing HEA, [TaNb]0.31(TiUHf)0.69, which is the first to include an actinide ion. Similar to the Zr-analogue, this material crystallizes in a body-centered cubic lattice with the lattice constant a = 3.41(1) Å and exhibits phonon mediated superconductivity with a transition temperatures Tc ≈ 3.2 K and upper critical fields Hc2 ≈ 6.4 T. These results expand this class of materials to include actinide elements, shows that superconductivity is robust in this sub-group, and opens the path towards leveraging HEAs as functional waste forms for a variety of radioisotopes.