Preheat oven to 375 degrees F. Line a baking sheet with parchment paper; set aside.
Heat oil in a large nonstick skillet over medium high heat. Season shrimp with salt and pepper, then sauté until pink and cooked through, about 1-2 minutes per side. Drain on a towel-lined plate; set aside.
Working with 1 phyllo sheet at a time and keeping the rest covered with a towel until ready to use, lay sheet out on a clean, dry work surface. Brush lightly with melted butter, then use a sharp knife to cut the sheet into quarters. Place one sheet on top of the other, making 2 doubled-up squares.
Place a shrimp in the center of each square, top with a piece of cream cheese, then a teaspoon of bacon, 1/2 teaspoon chives, and season with salt and pepper. Pull up the corners, gently twist together, use a chive to tie around purses and place on prepared baking sheet. Brush the purse lightly with butter. Repeat with remaining ingredients.
Bake purses for 10-12 minutes until golden and crisp.