By Janice Bitters Turi,

Salad-slinging restaurant chain Sweetgreen is set to start trading on the New York Stock Exchange Thursday, following an IPO that company leaders hope will price between $23 and $25 per share, valuing the startup at about $2.7 billion.

The Washington, D.C.-based company, which was founded in 2007, has 140 stores in 13 states, where it employs more than 5,000 people and tries to tap into what it describes as a grossly underserved market for fast-food that is also fresh, seasonal and healthy.

Its updated IPO prospectus, filed with the U.S. Securities and Exchange Commission last week, shows it’s expecting to double in size in the next three to five years after opening at...