  Dynamically studying Trans-Neptunian Object (TNO) binaries allows us to
measure masses and orbits. Most of the known objects appear to have only two
components, except (47171) Lempo which is the single known hierarchical triple
system with three similar-mass components. Though hundreds of TNOs have been
imaged with high-resolution telescopes, no other hierarchical triples (or
trinaries) have been found among solar system small bodies, even though they
are predicted in planetesimal formation models such as gravitational collapse
after the streaming instability. By going beyond the point-mass assumption and
modeling TNO orbits as non-Keplerian, we open a new window into the shapes and
spins of the components, including the possible presence of unresolved
``inner'' binaries. Here we present evidence for a new hierarchical triple,
(148780) Altjira (2001 UQ$_{18}$), based on non-Keplerian dynamical modeling of
the two observed components. We incorporate two recent Hubble Space Telescope
(HST) observations, leading to a 17 year observational baseline. We present a
new open-source Bayesian Point Spread Function (PSF) fitting code called nPSF
that provides precise relative astrometry and uncertainties for single images.
Our non-Keplerian analysis measures a statistically-significant
($\sim$2.5-$\sigma$) non-spherical shape for Altjira. The measured $J_2$ is
best explained as an unresolved inner binary and an example hierarchical triple
model gives the best fit to the observed astrometry. Using an updated
non-Keplerian ephemeris (which is significantly different from the Keplerian
predictions), we show that the predicted mutual event season for Altjira has
already begun with several excellent opportunities for observations through
$\sim$2030.
