Heat oven to 350°F; parchment-line two sheets. Whisk oats, flour, baking soda, and salt in bowl.
Beat butter, peanut butter, and sugars until creamy, about 2 minutes. Beat in egg and vanilla; mix in dry ingredients just until combined. Fold in chocolate chips.
Divide into 24 mounds, about 1 1/2 tablespoons each; space twelve on each sheet. Gently flatten to 1/2 inch thick.
Bake one sheet at a time 10 to 12 minutes until edges set and lightly browned. Rest on sheet 5 minutes; transfer to rack.
Cool completely; freeze in one layer until firm. Pack in freezer container with parchment between layers; freeze up to 2 months for best quality.
Thaw cookie at room temperature 20 to 30 minutes, or microwave on microwave-safe plate 10 to 15 seconds for softer center. Cool chocolate slightly before eating.