We present AlphaChute: a state-of-the-art algorithm that achieves superhuman performance in the ancient game of Chutes and Ladders. We prove that our algorithm converges to the Nash equilibrium in constant time, and therefore is -- to the best of our knowledge -- the first such formal solution to this game. Surprisingly, despite all this, our implementation of AlphaChute remains relatively straightforward due to domain-specific adaptations. We provide the source code for AlphaChute here in our Appendix.