One of the many hurdles facing lattice computations of quantities such as the hadronic vacuum polarization (HVP), are finite-volume effects. Since these are dominated by low-energy phenomena, they can be predicted and controlled using the low-energy effective field theory of QCD, Chiral Perturbation Theory (ChPT). In particular, it is estimated that at three loops, ChPT should reach enough precision to contribute to the ongoing calculations of the muon g-2. I present a major step toward this goal, namely the ChPT HVP amplitude in infinite volume. Besides laying the groundwork for the finite-volume calculation, this is an interesting quantity in its own right, with connections to many other processes via, e.g., its cuts. It is only the second three-loop calculation ever done in ChPT, and as a three-loop amplitude without propagating massless particles, it pushes the envelope of current loop integral technology, with novel integrals and relations having been found in the process of calculating it.