A Key Distribution Center enables secure communications among groups of users in a network by providing common keys that can be used with a symmetric encryption algorithm to encrypt and decrypt messages the users wish to send to each other. A Distributed Key Distribution Center is a set of servers of a network that jointly realize a Key Distribution Center. In this paper we propose an unconditionally secure scheme to set up a robust Distributed Key Distribution Center. Such a distributed center keeps working even if some minority of the servers malfunction or misbehave under the control of a mobile adversary. Our scheme for a distributed key distribution center is constructed using unconditionally secure proactive verifiable secret sharing schemes. We review the unconditionally secure verifiable secret sharing scheme described by Stinson and Wei, discuss a problem with the proactive version of that scheme, and present a modified version which is proactively secure.