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1
Place chicken in shallow bowl.
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2
Whisk next 5 ingredients in medium bowl.
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3
Pour over chicken; turn to coat.
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4
Cover; chill at least 1 hour and up to 6 hours, turning often.
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5
Whisk broth, juice, sugar, 3 tablespoons butter, tamarind paste, peel, and ginger in large saucepan.
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6
Boil mixture over medium-high heat until reduced to 3/4 cup and glaze coats back of spoon, stirring often, about 25 minutes. (Can be made 2 days ahead. Cool glaze, then cover and chill. Rewarm over medium heat, whisking occasionally.)
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7
Whisk in 3 tablespoons butter.
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8
Season glaze with salt and pepper.
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9
Prepare barbecue (medium-high heat).
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10
Reserve 1/4 cup glaze in bowl.
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11
Grill chicken until cooked through, basting with reserved glaze, about 5 minutes per side.
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12
Arrange chicken atop rice on platter.
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13
Spoon remaining glaze over chicken.
