The harmonic magnon modes in a Heisenberg ferromagnetic chain in a random weak field are studied. The Lyapunov exponent for the uniform (Ic = 0) mode is computed using the coherent potential approximation (CPA) in the weak-disorder limit. The CPA results are compared with the numerical and weak-disorder expansions of various random systems. We have found that the inverse localization length and the integrated density of states have anomalous power law behaviour as reported earlier. The CPA also reproduces the dispersion law for the same system, calculated by Pimentel and Stinchcombe using the real space renormalization scaling technique. A brief comment is also made for the uniform weak-field case.