A ³⁵Cl Zeeman NQR study of a single crystal of boron trichloride yields the value of the field-gradient asymmetry parameter of 0.557 ±0.01, in agreement with previous values of 0.54 and 0.50 obtained from studies of polycrystalline samples. Apart from the well known doublet due to an isotope effect, further fine structure whose details depend on the orientation of the Zeeman field is observed. It is shown that this fine structure arises from ¹¹B-³⁵Cl dipole-dipole interaction.