  Early Dark Energy (EDE) is a prominent model to resolve the Hubble tension,
which employs a dynamical axion with a periodic potential. In this work, we
take first steps towards the embedding of this model into stable
compactifications of string theory. First, we provide a pedagogical review of
the EDE scenario and its main challenges. Second, we construct a simple
supergravity toy model using only minimal ingredients. Already at this level,
we can understand the origin of the harmonics of the EDE scalar potential in
terms of a delicate balance of the leading terms from separate non-perturbative
effects. Third and final, we embed the model into a KKLT-type compactification,
with the EDE scalar field realized by a two-form axion. We find that a
successful embedding, with all moduli stabilized, requires restrictive
assumptions both on the Pfaffians and on the exponents of the non-perturbative
terms responsible for the EDE dynamics. We point out that such non-generic
conditions reflect well known challenges of the EDE model and further
investigation might guide us towards a conclusive resolution.
