  The notion of Bohr chaos was introduced in [3, 4]. We answer a question
raised in [3] of whether a non uniquely ergodic minimal system of positive
topological entropy can be Bohr chaotic. We also prove that all systems with
the specification property are Bohr chaotic, and by this line of thought give
an independent proof (and stengthening) of theorem 1 of [3] for the case of
invertible systems. In addition, we present an obstruction for Bohr chaos: a
system with fewer than a continuum of ergodic invariant probability measures
cannot be Bohr chaotic.
