The ground-state rotational spectrum of the dimethyl ether dimer, (DME)(2), has been studied by molecular beam Fourier transform microwave and free jet millimeter wave absorption spectroscopies. The molecular beam Fourier transform microwave spectra of the (DME-d(6))(2), (DME-C-13)(2), (DME-d(6))... (DME), (DME-C-13)...(DME), and (DME)..(DME-C-13) isotopomers have also been assigned. The rotational parameters have been interpreted in terms of a C. geometry with the two monomers bound by three weak C-H... 0 hydrogen bonds, each with an average interaction energy of about 1.9 kJ/mol. The experimental data combined with high-level ab initio calculations show this kind of interaction to be improper, blue-shifted hydrogen bonding, with an average shortening of the C-H bonds involved in the hydrogen bonding of 0.0014 Angstrom. The length of the C-H...O hydrogen bonds, r(O...H), is in the range 2.52-2.59 Angstrom.