At dawn in Xochimilco, home to Mexico City’s famed floating gardens, farmers in muddied rain boots squat among rows of beets as a group of chefs arrive to sample sweet fennel and the pungent herb known as epazote.

By dinnertime some of those greens will be on plates at an elegant bistro 12 miles (20 kilometers) to the north, stewed with black beans in a $60 prix-fixe menu for well-heeled diners.

Call it floating-farm-to-table: A growing number of the capital’s most in-demand restaurants are incorporating produce grown at the gardens, or chinampas, using ancient cultivation techniques pioneered hundreds of years ago in the pre-Columbian era.

While sourcing local ingredients has become fashionable for many top chefs around the globe, it takes on additional significance in Xochimilco (so-chee-MIL-co), where a project linking chinampa farmers with high-end eateries aims to breathe life and a bit of modernity into a fading and threatened tradition.

“People sometimes think (farm-to-table) is a trend,” said Eduardo Garcia, owner and head chef of Maximo Bistrot in the stylish Roma Norte district. “It’s not a trend. It’s something that we humans have always done and we need to keep doing it, we need to return to it.”

Xochimilco, on the far southern edge of Mexico City, is best-known as the “Mexican Venice” for its canals and brightly colored boats where locals and…