Delhi is a rarity on the Indian landscape: a symbol of urban progress rather than urban decay. And for almost a decade, Sheila Dikshit has presided over the nation’s capital as its chief minister.

Dikshit, nearing the end of an unprecedented second term, has helped guide an array of economic and political changes. Under her watch, the first phase of the Delhi Metro was completed on budget and on time—a feat heralded as belying the stereotype of the Indian government’s inefficiency. The second phase is on track to be completed in time for the Commonwealth Games, scheduled to take place in the city in 2010.

Also during her tenure, power distribution has been privatized, pollution reduced, and green areas throughout the city increased. Students at government schools are performing better. In addition, Dikshit has attempted to lessen the tensions between the bureaucracy and citizens through an initiative that brings both sides together for regular discussions. Bhagidari, as it is called, has been held up as an international model of good governance.

Yet Dikshit would be among the first to acknowledge that progress has not come fast enough or without snags. Delhi is straining under the weight of a vast and...