When Di’Zhon Chase’s teacher told her that she might be able to enroll in a Harvard University class, she was skeptical — and not just because the Ivy League school was more than 2,000 miles from her hometown, Gallup, N.M.

“Harvard isn’t part of the conversation — you don’t even hear that word in Gallup,” Ms. Chase said. “It isn’t something that adults expect out of us. I don’t think it’s because they don’t believe in us; it’s just so much is stacked against us.”

But in fall 2019, Ms. Chase joined a small group of students across the country in an experiment that sought to redefine what is possible for students who share her underprivileged background. Through an initiative started by a New York-based nonprofit, the National Education Equity Lab, hundreds of students are virtually rattling the gates of some of the nation’s most elite colleges by excelling in their credit-bearing courses before they leave high school.

The Equity Lab enrolled more than 300 11th and 12th graders from high-poverty high schools in 11 cities across the country in a Harvard course, “Poetry in America: The City From Whitman to Hip-Hop,” taught by a renowned professor, Elisa New. The high schoolers met the same rigorous standards of the course created for Harvard’s admitted students — they listened to lectures, took quizzes and completed essays, and they were graded by the same standards.

The goal of the pilot program was “reimagining and expanding the roles and responsibilities of universities,” and encouraging them to pursue star students from underprivileged backgrounds “with the same enthusiasm and success with which they identify top athletes,” said Leslie Cornfeld, the Equity Lab’s founder and chief executive.

For decades, programs such as QuestBridgehave tried to connect promising underprivileged students to elite higher education, with some success, but the Equity Lab effort is less about matchmaking than challenging students academically, giving them confidence and preparing them for the rigors of competitive colleges.

The early results, Ms. Cornfeld said, are clear: “Our nation’s talent is evenly distributed; opportunity is not.”