In this work, we study the dynamical properties of Krystyna

Kuperberg's aperiodic flows on 3-manifolds. We introduce

the notion of a "zippered lamination," and with suitable

generic hypotheses, show that the unique minimal set for

such a flow is an invariant zippered lamination. We obtain a

precise description of the topological and dynamical properties

of the minimal set, including the presence of non-zero

entropy-type invariants and chaotic behavior. Moreover, we

show that the minimal set does not have stable shape, yet

satisfies the Mittag-Leffler condition for homology groups.