We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.