This all has to do with intermolecular forces. To determine which intermolecular forces act on a certain group of molecules, one must look at the molecular geometry of an individual molecule. In this case, both #CH_4# and #CH_3Cl# have the same molecular geometry, called tetrahedral geometry.
This means each one has a central carbon atom and its surrounded by four atoms that are equally spaced from it. The one difference between the two molecules is the electronegativity of the atoms that compose each one.
Since #CH_4# has four hydrogen atoms surrounding it and each hydrogen atom has the same electronegativity, there is no net charge on the molecule. This means that it connects very weakly with the other #CH_4# molecules that surround it.
Conversely, #CH_3Cl# has a central carbon that is surrounded by three hydrogen atoms and one chlorine atom. Now the hydrogens still have the same electronegativity as one another, but the chlorine atom has a high difference in electronegativity compared to the hydrogens. To be specific, hydrogen has an electronegativity value of 2.1 and chlorine has a value of 3.0.
Since chlorine is more electronegative, the electrons in the molecule of #CH_3Cl# are more likely to exist around the chlorine atom than the hydrogen atoms. This gives an individual #CH_3Cl# molecule a side that is more negative than the other, otherwise known as a dipole moment.
Since every #CH_3Cl# molecule is like this, the #CH_3Cl# molecules can form stronger bonds with each other, having the partially negative end of one molecule form bonds with the partially positive end of another molecule.
These bonds require more energy to be absorbed by a sample of #CH_3Cl# molecules before the molecules transition from one physical state to another, since state changes require the weakening of bonds. More energy required to break a bond means a higher temperature for a phase change, in this case a higher boiling point.
