Does the electrolysis of water produce chlorine gas? http://orbitingfrog.com/2014/11/02/electrolysis-of-water-with-pencils-and-a-9v-battery/

This article seems to indicate that "a small amount of Chlorine may be produced as you [perform electrolysis on water]". Is this true? I thought it was just H2 and O2 produced.
It's the tablespoon of salt he added, giving the chlorine when electrolysis is done. I have done electrolysis with salt-free water (though a bit acidic to get the water to electrolyze faster) and chlorine was nowhere to be found.

Electrolysis of saltwater produces hydrogen and chlorine; and leaves sodium hydroxide behind.