Combine first 4 ingredients (through milk) in a medium saucepan. Bring to a simmer over medium heat, stirring frequently. Cook until sugar dissolves, stirring gently (about 2 minutes).
Remove from heat; add chocolate chips.
Let stand 1 minute; stir with a whisk until chips are melted.
Add peanut butter and vanilla; stir well with a whisk. Stir in oats. Cool slightly.
Drop mixture by tablespoonfuls onto wax paper; cool 15 minutes or until firm.