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Rinse rice in a bowl with several changes of cold water until water runs clear as it is poured off. Add enough cold water to cover rice by 2 inches and let stand at room temperature at least 8 hours.
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Rinse urad dal in a bowl with several changes of cold water until water runs clear as it is poured off. Add enough cold water to cover urad dal by 2 inches and let stand at room temperature at least 8 hours.
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Drain rice, then put in a blender with 1 cup water and puree until smooth, about 2 minutes. Transfer puree to a large bowl.
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Drain urad dal, then put in blender (no need to clean) with 2/3 cup water and puree until smooth, about 2 minutes. Stir into rice puree along with salt. Cover with plastic wrap and let mixture ferment at warm room temperature until foamy and doubled in bulk, about 24 hours.
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Heat griddle or skillet over medium-high heat until hot, then reduce heat to medium. Stir batter and pour 1/2 cup into center of griddle with a ladle, then starting from center, spread batter to a 12-inch circle by moving back of ladle in a circular motion from center to edge. As batter sets, pour 1 teaspoon oil around edge and on top of dosa to help loosen, then when batter is completely set and underside is pale golden, 1 1/2 to 2 minutes, transfer dosa with a spatula to a plate. Sprinkle with chile powder and fold in half.
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Continue making dosas in same manner, serving dosas as made or keeping warm between layers of foil in a low oven.
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Serve dosa with coconut chutney.
