Ayse Giray sued Ulukaya in 2012, saying she's entitled to a controlling stake in the biggest Greek-style yogurt maker in the U.S. A New York state judge is set to hear arguments Tuesday over one of the key ingredients of her suit: that she was a part-owner of the feta cheese maker that she alleges was used by her ex-husband to start Chobani. The case could spoil any plans Chobani has for a public offering, said Sam Hamadeh, the founder and chief executive officer of Privco Media LLC, a New York-based firm that tracks private companies.