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

Methane (CH4) — London dispersion forces

Dimethyl ether (CH3OCH3) — dipole-dipole attractions

Methanol (CH3OH) — hydrogen bonding

Therefore, Methanol - CH3OH with H-Bonding have highest Boiling Point among the given chemical compounds.