There is currently a (possible) tension between various measurements of the Hubble expansion rate. I will give a recap of this issue, and describe  how we use the Cosmic Microwave Background to infer the local expansion rate. I will explain what assumptions we usually make about the cosmological model in doing so, and what kinds of early-universe modifications could bring some of the different measurements better in line. I will talk about new measurements we are making in Chile to improve estimates of the Hubble constant from the CMB, and to test alternative models.