MEXICO CITY—“Clau-dia! Clau-dia! Clau-dia!” The crowd swarms around the smiling woman, chanting her name as she makes her way from her car to the stage at a recent campaign rally in a ramshackle neighborhood of cinder block buildings. Voters jostle to clasp her hands, look in her eyes, and tell her about their troubles.

The enthusiasm still astonishes Claudia Sheinbaum Pardo. “It’s like I’m an actress, or someone actually famous!” she says. Until 3 years ago, she worked quietly as an environmental engineer at the National Autonomous University of Mexico (UNAM) here. Now, with a 20-point lead in the polls ahead of the 1 July elections, she seems set to become mayor of this city of nearly 9 million people.

Sheinbaum Pardo considers herself a researcher first and foremost. Her work on energy science and engineering—with a focus on vehicle emissions and climate change mitigation—is respected both in Mexico and abroad, and she’s a member of the Mexican Academy of Sciences and a former member of the United Nations Intergovernmental Panel on Climate Change (IPCC). Many say she’s uniquely positioned to understand and tackle the myriad problems afflicting this megacity, especially its stuffed-to-the-gills public transportation, epic traffic snarls, and worsening water crisis.