  Local heights are arithmetic invariants used in the quadratic Chabauty method
for determining the rational points on curves. We present an algorithm to
compute these local heights for hyperelliptic curves at odd primes $\ell\neq
p$. This algorithm significantly broadens the applicability of quadratic
Chabauty to curves which were previously inaccessible due to the presence of
non-trivial local heights. We provide numerous examples, including the first
quadratic Chabauty computation for a curve having two primes with non-trivial
local heights.
