Preheat oven to 325 degrees F. Grease an 9 x 13 pan.

Melt butter. Sauté garlic and ham until ham is lightly browned. Add broth, milk and chives and bring to a boil. Reduce heat; add cornmeal and whisk until thickened. Switch to spoon near end.

Remove polenta from heat and beat in cheese. Spread polenta in greased pan, smoothing surface. (Can be refrigerated at this point and browned before serving.)

Bake 20 minutes until set and lightly browned.

Cool slightly. Cut into squares