The first precise ground-state dipole moment of CaCl was measured by using the molecular-beam laser-microwave double-resonance method. From the study of two vibrational states the vibrational dependence =0+1(v+12) was determined. The result is 0=4.257(3) D and 1=0.016(3) D (with statistical standard deviation in the last digit given in parentheses). The determination of the dipole moment from measured Stark shifts of individual hyperfine levels required diagonalization of the complete energy matrix. Problems in the application of the Rittner ionic model to the alkalineearth monohalides are discussed.