  About a dozen exoplanetary systems have been discovered with three or more
planets participating in a sequence of mean-motion resonances. The unique and
complex architectures of these so-called "resonant chains" motivate efforts to
characterize their planets holistically. In this work, we perform a
comprehensive exploration of the spin-axis dynamics of planets in resonant
chains. Planetary spin states are closely linked with atmospheric dynamics and
habitability and are thus especially relevant to resonant chains like
TRAPPIST-1, which hosts several temperate planets. Considering a set of
observed resonant chains, we calculate the equilibrium states of the planetary
axial tilts ("obliquities"). We show that high obliquity states exist for
$\sim60\%$ of planets in our sample, and many of these states can be stable in
the presence of tidal dissipation. Using case studies of two observed systems
(Kepler-223 and TOI-1136), we demonstrate how these high obliquity states could
have been attained during the initial epoch of disk-driven orbital migration
that established the resonant orbital architectures. We show that the
TRAPPIST-1 planets most likely have zero obliquities, with the possible
exception of planet d. Overall, our results highlight that both the orbital and
spin states of resonant chains are valuable relics of the early stages of
planet formation and evolution.
