Place chicken stock in a medium pan and bring to a boil. Pour cornmeal into the boiling stock in a thin stream, whisking as you pour.
Reduce the heat to a simmer and cook for about 40 minutes, stirring frequently. Add up to 1 cup more water as necessary, to keep soft enough to stir. Grains should be swollen and taste cooked, not raw.
Add salt, butter, goat cheese, and rosemary. Stir until melted.
Remove from heat, cover, and let stand 5 minutes to thicken.