Ultracompact H II regions have sizes of order 0.1 pc. The ionized gas within has sound speed c<SUB>s</SUB> ̃ 10 km s<SUP>-1</SUP>, so they should have dynamical times of order 10<SUP>4</SUP> yr. However, there are roughly 10% as many ultracompact H II regions as there are OB stars in the Galaxy, suggesting lifetimes an order of magnitude longer. Proposed solutions have included confinement by thermal pressure or ram pressure. We have used ZEUS-MP to perform 3D dynamical simulations of the expansion of an H II region in a gravitationally collapsing core embedded in a turbulent flow to examine this problem. We find that the expanding H II region breaks out of the core into lower density gas in a dynamical time, suggesting that pressure confinement is ineffective. However, the swept up shell is itself gravitationally unstable. The new cores that form can be ionized externally by the central star, even if they are too small to form an OB star themselves. Although these new ultracompact H II regions only last a dynamical time themselves, new ones can form repeatedly during the expansion of the shell to parsec scales over a timescale of 10<SUP>5</SUP> yr, potentially solving the lifetime problem. We present maps of emission measure from our models to demonstrate that this scenario generally agrees with recent observations showing that ultracompact H II regions are almost always associated with more extended emission from ionized gas. This work was partially supported by NSF Career grant AST99-85392 and NASA grants NAG5-10103 and NAG5-13028. Computations were performed at the Pittsburgh Supercomputer Center, supported by NSF, and on an Ultrasparc III cluster generously donated by Sun Microsystems.