Which of the following chemical compounds has the highest boiling point?

Chemical Compounds with stronger intermolecular forces have higher boiling points.

The order of strengths of intermolecular forces is:

 London dispersion < dipole-dipole < H-bonding

${\text{Methane (CH}}_{\mathrm{4)}}$ ? London dispersion forces

${\text{Dimethyl ether (CH}}_3{\text{OCH}}_{\mathrm{3)}}$ ? dipole-dipole attractions

${\text{Methanol (CH}}_3\text{OH)}$ ? hydrogen bonding

Therefore, ${\text{Methanol -}}^{}$${\text{CH}}_3\text{OH}$$\text{with H-Bonding have highest Boiling Point among the given chemical compounds.}$