In a medium bowl, cream together butter, oil, and sugar. Add vanilla, salt, and egg white; mix thoroughly to combine.
In a small bowl, mix together flour and baking soda; stir into batter. Add chocolate chips to batter; stir to distribute evenly throughout.
Drop rounded half-teaspoons of dough onto one or two large nonstick baking sheets, leaving a small amount of space between each cookie. Bake cookies until golden around edges, about 4 to 6 minutes; cool on a wire rack.