A C*-algebra is said to be Z-stable if it tensorially absorbs the Jiang-Su algebra Z. In particular, given an algebra A in the classifiable class, the Elliot invariant cannot distinguish between A and A tensor Z, so we require that classifiable algebras be Z-stable. Now suppose we have an extension 0->I->E->J->0, and we know that I and J are both Z-stable. A natural question is whether E is still Z stable. We provide an affirmative answer for the case where E is unital. This talk is based on joint work with George Elliott and Zhuang Niu.