The inference of the present expansion rate from the Cosmic Microwave Background (CMB) and other early-time probes (assuming standard cosmology) is in significant tension with several direct measurements of the same quantity. If this discrepancy is not due to unresolved systematics, it could provide strong evidence for physics beyond the standard models (SM) of particle physics and cosmology. In a recent work Cyr-Racine, Ge and Knox pointed out a strong degeneracy in the evolution equations describing the CMB that, under certain strong assumptions, enables one to resolve the tension. A physical implementation of this degeneracy requires the introduction of a hidden sector with several puzzling features: 1) low-energy field content that is nearly identical to the SM, 2) similar energy density ratios between different components as in the visible sector and 3) recombination of dark states that is simultaneous with standard hydrogen recombination. I will describe a model based on a partial copy of the SM with asymmetric reheating where these features arise naturally. Both our model and the original proposal of Cyr-Racine, Ge and Knox require a significantly lower helium fraction than is directly observed in the late universe. Thus, the Hubble tension is shifted to a helium one.