A theoretical analysis is presented that shows how the dynamic instability of microtubules in combination with microtubule polymerization forces provides a microtubule organizing center with a mechanism to position itself at the center of a confining geometry. The rate of approach to the center and the positional preciseness depend on the parameters that characterize dynamic instability, the size of the confining region, and the number of microtubules. Fastest positioning occurs when on average one microtubule is in contact with one of the confining barriers. The potential relevance of this mechanism to the positioning of microtubule organizing centers in cells is discussed.