  In this article we introduce a new class of Rolewicz-type operators in l_p,
$1 \le p < \infty$. We exhibit a collection F of cardinality continuum of
operators of this type which are chaotic and remain so under almost all finite
linear combinations, provided that the linear combination has sufficiently
large norm. As a corollary to our main result we also obtain that there exists
a countable collection of such operators whose all finite linear combinations
are chaotic provided that they have sufficiently large norm.
