Originally Posted by FBinNY

Besides the normal chordal action, other causes include slightly imperfect sprocket formation (a likely cause if it only vibrates on a single sprocket, not the smallest).

Another possibility is chainline, combined with the shapes of the chain inner plates and the sprockets. When the chain is feeding at an angle, the outer plates can move over on the teeth, then the next inner plate can engage or disengage badly bump or slipping off the tooth's edge, and going back to the line. Some chains have bellmouth formed into the inner plates to smooth this out, others, less so. You can see the effect if you turn the pedals in SloMo, and observe the position of the tooth as the chain engages.

Both the above issues self resolve over time as wear smooths all the rough edges.