Ab initio molecular orbital methods are used to determine the fraction eB/e of the full protonic charge carried by the Bjerrum defect in ice. This can be accomplished by calculating the change in dipole moment after a defect has been transported. Dipole moments are calculated for a series of linear chains of water molecules and the results extrapolated to infinite chain length. Known deficiencies of the two basis sets used are accounted for by scaling the results against the experimentally determined dipole moment of water. Also, the effect of the three-dimensional hydrogen-bonded network of ice is estimated by including additional water molecules as branches of the chain. These extra bonds, whether present as terminal branches or as closed rings, result in a decrease of only several percent in eB, the charge transmitted by OH bond rotations. Other variations in the calculations include elongation of the OH bond length in ice from 0.97 to 1.01 Å, which produces a net increase in eB of 6%, and reduction of the HOH bond angle in each water molecule to 104.5°, which results in a smaller increase. Taking into account the various sources of error and uncertainties as to the precise geometry leads to a value of eB = 0.36 ± 0.03, which is in satisfactory agreement with the values obtained in a completely different way from dielectric measurements.