The ground-state rotational spectra of five isotopomers of the 'charge-transfer' complex H3N...Cl2 have been observed by pulsed-nozzle, Fourier-transform microwave spectroscopy. The complex has C3v symmetry with the nuclei in the order H3N...Cl-Cl. A detailed analysis of the Cl nuclear quadrupole hyperfine structure in transitions of H-3 N-15...Cl-35(2), H-3 N-15...Cl-35 Cl-37, and H-3 N-15...Cl-37 Cl-35 gave the rotational constant, B(o), the centrifugal distortion constants D(J) and D(JK), and the nuclear quadrupole coupling constants chi(Cl(i)) and chi(Cl(o)) (i = inner, o = outer) in each case. The distance r(N...Cl(i) was obtained by an r(s)-type method and an r(o)-type method and lies in the range 2.73 +/- 0.03 angstrom. A detailed analysis that allowed for bond shrinkage on isotopic substitution in the Cl-35(2) subunit of H-3 N-15...Cl-35(2) gave the r(s)-type coordinates of Cl(i) and Cl(o) and hence the distance r(s) (Cl-Cl) = 2.00 angstrom. This value is very close to that in free Cl2 and indicates only a slight perturbation of this subunit when the complex is formed. The relatively small intermolecular stretching force constant, k(sigma) = 12.71(3) N m-1 determined from D(J) and the weak perturbation of chi(Cl(i)) and chi(Cl(o)) from the value in free Cl2, reinforce this conclusion. The observed difference chi(Cl-35(o)) - chi(Cl-35(i)) = 13.99 MHz can be interpreted in terms of a transfer of 0.064e from Cl(i) to Cl(o) on formation of H-3 N-15...Cl-35(2). It seems likely that the molecular interaction is mainly electrostatic in origin and charge-transfer effects are small.