Accumulation of moderated positrons in a static Penning trap is observ
ed for surprisingly long collection intervals. Stochastic transport be
tween axial and transverse motion provides the requisite additional ph
ase space to explain the observed trapping. An understanding of this t
ransport mechanism can be used to improve a variety of charged particl
e traps. Moreover, this system presents a new opportunity to study the
onset of chaos.