<p>The classical Chern correspondence states that a choice of Hermitian metric on a holomorphic vector bundle determines uniquely a unitary ‘Chern connection’. We generalize the Chern correspondence to the context of higher gauge theory, where the structure group of the bundle is categorified. For this, we define connective structures on multiplicative gerbes and propose a natural notion of complexification for an important class of 2-groups. Using this, we put forward a new notion of connection which is well-suited for describing holomorphic principal 2-bundles for these 2-groups, and apply it to establish a Chern correspondence. This relates holomorphic principal 2-bundles with holomorphic connective structure to supersymmetric configurations in string theory.</p>