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Previous studies of the galactic habitable zone have been concerned with identifying those regions of the Galaxy that may favor the emergence of complex life. A planet is deemed habitable if it meets a set of assumed criteria for supporting the emergence of such complex life. In this work, we extend the assessment of habitability to consider the potential for life to further evolve to the point of intelligence--termed the propensity for the emergence of intelligent life, φI. We assume φI is strongly influenced by the time durations available for evolutionary processes to proceed undisturbed by the sterilizing effects of nearby supernovae. The times between supernova events provide windows of opportunity for the evolution of intelligence. We developed a model that allows us to analyze these window times to generate a metric for φI, and we examine here the spatial and temporal variation of this metric. Even under the assumption that long time durations are required between sterilizations to allow for the emergence of intelligence, our model suggests that the inner Galaxy provides the greatest number of opportunities for intelligence to arise. This is due to the substantially higher number density of habitable planets in this region, which outweighs the effects of a higher supernova rate in the region. Our model also shows that φI is increasing with time. Intelligent life emerged at approximately the present time at Earth's galactocentric radius, but a similar level of evolutionary opportunity was available in the inner Galaxy more than 2 Gyr ago. Our findings suggest that the inner Galaxy should logically be a prime target region for searches for extraterrestrial intelligence and that any civilizations that may have emerged there are potentially much older than our own.