Add fregula and salt; cook 1 minute, stirring constantly. Stir in wine; cook 30 seconds or until liquid is nearly absorbed, stirring constantly.
Set aside 1/4 cup broth mixture; cover and keep warm.
Add remaining broth mixture, 1/2 cup at a time, stirring constantly until each portion of broth is absorbed before adding the next (about 15 minutes total).
Remove from heat.
Stir in reserved 1/4 cup broth mixture, chives, goat cheese, and 1 1/2 teaspoons abbamele.