Alpek SAB, Mexico’s largest privately owned petrochemical company, is planning the nation’s biggest ever initial public offering, ending a nine-month lull in new listings.

Alfa SAB, the conglomerate that also owns auto-parts and processed-foods companies, is selling a stake in Alpek after Mexico’s benchmark index rallied to a record high this month and Brazil and Colombia snapped IPO droughts. Alfa plans to raise as much as $851 million from the sale of 17.9 percent of Alpek, which makes polyester fiber used in clothing and expandable polystyrene for packing material.