We study the general behaviour of the correlation length for the two-point correlation function of the local fields in an Ising chain with binary distributed fields. At zero field it is shown that is the same as the zero-field correlation length for the spin - spin correlation function. For the field-dominated behaviour of we find an exponent for the power-law divergence which is smaller than the exponent for the spin - spin correlation length. The entire behaviour of the correlation length can be described by a single crossover scaling function involving the new critical exponent.