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Mix the shredded chicken, pesto and cheese together in medium-sized mixing bowl.
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Open the cans of crescent rolls and separate the dough into large rectangles. Press the perforated edges together.
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Spoon about 1/4 cup of the chicken mixture into the center of each rectangle.
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Fold the dough over the top of the chicken mixture, one corner at a time, until the mixture is well-covered and there are no holes. Stretch the dough as necessary.
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Place the chicken balls onto an un-greased cookie sheet. Brush with olive oil and sprinkle with Italian seasoning if desired.
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Bake at 375 degrees for 12-15 minutes, until the tops of the chicken balls are golden brown.