  How much time does a tunneling particle spend in a barrier? A Larmor clock,
one proposal to answer this question, measures the interaction between the
particle and the barrier region using an auxiliary degree of freedom of the
particle to clock the dwell time inside the barrier. We report on precise
Larmor time measurements of an ultra-cold gas of $^{87}$Rb atoms tunneling
through an optical barrier. The data capture distinctive features that confirm
longstanding predictions of tunneling times. In particular, we demonstrate that
atoms spend less time tunneling through higher barriers and that this time
decreases for lower energy particles. For the lowest measured incident energy,
at least $90\%$ of transmitted atoms tunneled through the barrier, spending an
average of $0.59(2)$ms inside. This is $0.11(3)$ms faster than atoms traversing
the same barrier with energy close to the barrier's peak and $0.21(3)$ms faster
than when the atoms traverse a barrier with $23\%$ less energy.
