Yup, a classic case of chatter.
It's happens when the tool bit digs into the work and then releases. If that happens at the natural frequency of the structure supporting it ,in this case your tool post, compound rest and saddle, it will resonate; sort of like playing the violin. You can get rid of it by changing the natural frequency of the set-up. Change the rpm of the spindle, move the workpiece farther into the chuck, grind a smaller radius on the point of the tool, reduce the amount of tool overhang, or maybe even tighten the gibs in your cross slide and compound rest. Some or all of those things may be required.
Let us know what worked for you.
Tom