The microwave spectra of six isotopomers of HCCH . N2O have been measured. The structure of the complex has been fully determined. The monomers have a planar, nearly parallel orientation. They deviate from parallel by 13.6 degrees, and the tilt moves the oxygen end of the N2O closer to the acetylene, The centers of mass of the two monomers are separated by 3.2961(8) Angstrom. The dipole moment of the HCCH .(N2O)-N-15 isotope has been measured, giving mu(a) = 0.0915(7) D, mu(b) = 0.1503(19) D, and mu(tot) = 0.1759(16) D. The conclusions of this work refine previous experimental and semiempirical studies. New semiempirical calculations using a different model agree well with the current results.