  The precise value of the mean neutron lifetime, $\tau_n$, plays an important
role in nuclear and particle physics and cosmology. It is a key input for
predicting the ratio of protons to helium atoms in the primordial universe and
is used to search for new physics beyond the Standard Model of particle
physics. There is a 3.9 standard deviation discrepancy between $\tau_n$
measured by counting the decay rate of free neutrons in a beam (887.7 $\pm$ 2.2
s) and by counting surviving ultracold neutrons stored for different storage
times in a material trap (878.5$\pm$0.8 s). The experiment described here
eliminates loss mechanisms present in previous trap experiments by levitating
polarized ultracold neutrons above the surface of an asymmetric storage trap
using a repulsive magnetic field gradient so that the stored neutrons do not
interact with material trap walls and neutrons in quasi-stable orbits rapidly
exit the trap. As a result of this approach and the use of a new in situ
neutron detector, the lifetime reported here (877.7 $\pm$ 0.7 (stat) +0.4/-0.2
(sys) s) is the first modern measurement of $\tau_n$ that does not require
corrections larger than the quoted uncertainties.
