  The discrepancy between the values of the Hubble constant $H_0$ derived from
the local distance ladder and the cosmic microwave background provides a
tantalising hint of new physics. We explore a potential resolution involving
screened fifth forces in the local Universe, which alter the Cepheid
calibration of supernova distances. In particular, if the Cepheids with direct
distance measurements from parallax or water masers are screened but a
significant fraction of those in other galaxies are not, neglecting the
difference between their underlying period--luminosity relations biases the
local $H_0$ measurement high. This difference derives from a reduction in the
Cepheid pulsation period and possible increase in luminosity under a fifth
force. We quantify the internal and environmental gravitational properties of
the Riess et al. distance ladder galaxies to assess their degrees of screening
under a range of phenomenological models, and propagate this information into
the $H_0$ posterior as a function of fifth force strength. We consider
well-studied screening models in scalar--tensor gravity theories such as
chameleon, K-mouflage and Vainshtein, along with a recently-proposed mechanism
based on baryon--dark matter interactions in which screening is governed by
local dark matter density. We find that a fifth force strength $\sim5-30\%$
that of gravity can alleviate (though not resolve) the $H_0$ tension in some
scenarios, around the sensitivity level at which tests based on other distance
ladder data can constrain this strength. Although our analysis is exploratory
and based on screening models not necessarily realised in full theories, our
results demonstrate that new physics-based local resolutions of the $H_0$
tension are possible, supplementing those already known in the
pre-recombination era.
