Preheat broiler. Line heavy baking sheet with foil. Arrange tomatillos on prepared sheet. Broil until tomatillos blacken in spots, turning once, about 5 minutes per side.

Transfer tomatillos and any juices on sheet to processor and cool. Add chiles and garlic to processor and blend until smooth puree forms.

Heat oil in medium saucepan over medium-high heat. Add tomatillo puree and boil 5 minutes, stirring often. Add broth. Reduce heat to medium; simmer until sauce coats spoon thickly and is reduced to 1 cup, stirring occasionally, about 40 minutes. Season with salt. Mix in chicken and cilantro. (Can be made 1 day ahead. Cover and chill.)