Operator valued free probability theory was developed in the 1990's as a method of encoding amalgamated free product phenomenon in operator algebras in a probabilistic setting. As in the case of scalar valued free probability, this theory may be developed along similar lines as classical probability theory, with many classical theorems having free analogues. In classical probability theory, it was proven by Hincin that a probability measure that is the weak limit of the convolution of an infinitesimal array of probability measures is necessarily infinitely divisible. We will provide an alternative proof of this theorem utilizing the Steinitz Lemma. We will then use this approach to prove an analogous result in the field of operator valued free probability theory.