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1
Cut the stems from the Swiss chard leaves and chop them and the leaves separately.
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2
In a large skillet cook the garlic in the oil over moderate heat, stirring, until it is fragrant, stir in the Swiss chard stems and 1/4 cup water, and cook the mixture, covered, for 5 minutes.
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3
Add the leaves and cook the mixture, covered, stirring occasionally, for 3 to 5 minutes, or until the leaves are tender.
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4
Drain the Swiss chard mixture in a bowl toss it with the shredded chicken and salt and pepper to taste.
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5
In a skillet heat 1/4 inch of the oil over moderately high heat until it is hot but not smoking, in it fry the tortillas, 1 at a time, turning them, 3 to 4 seconds, or until they are softened, and transfer them with tongs as they are fried to paper towels to drain.
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6
In a bowl thin the tomato sauce with the broth, spoon about 1/3 cup of it into the bottom of a greased 13- by 9-inch baking dish, and arrange 4 of the tortillas in one layer over it.
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7
Spread the tortillas with half the chicken mixture and half the Monterey Jack, spoon about 1/2 cup of the remaining sauce over the mixture, and cover it with 4 of the remaining tortillas in one layer.
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8
Spread the tortillas with the remaining chicken mixture and the remaining Monterey Jack, top the mixture with 1/2 cup of the remaining sauce, and cover it with the remaining 4 tortillas.
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9
Pour the remaining sauce evenly over the tortillas and sprinkle it with the Parmesan.
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10
Bake the enchiladas, covered with foil, in the middle of a preheated 350F.
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11
oven for 15 minutes, remove the foil, bake the enchiladas, uncovered, for 5 to 10 minutes more, or until the cheese is bubbling.
