  We experimentally measure, and theoretically analyze the three-atom
recombination rate, $L_3$, around a narrow $s$ wave magnetic Feshbach resonance
of $^6$Li-$^6$Li at 543.3 Gauss. By examining both the magnetic field
dependence and especially the temperature dependence of $L_3$ over a wide range
of temperatures from a few $\mu$K to above 200 $\mu$K, we show that three-atom
recombination through a narrow resonance follows a universal behavior
determined by the long-range van der Waals potential, and can be described by a
set of rate equations in which three-body recombination proceeds via successive
pairwise interactions. We expect the underlying physical picture to be
applicable not only to narrow $s$ wave resonances, but also to resonances in
nonzero partial waves, and not only at ultracold temperatures, but also at much
higher temperatures.
