Why would chloroethane have a lower boiling point than ethane?

That is not true. Chloroethane has a greater boiling point than ethane.

This is due to the greater intermolecular attraction forces.

The greater electronegativity of Cl than C's, creates a stronger atraction of the electron cloud toward Cl, driving to the formation of permanent dipoles.

Then, in addition to the dispersion forces (present in the ethane and chlorometane) there are forces due to the attraction between the permanent dipoles, which cause a higher boiling point.