An exact conformal model representing a constant magnetic field backgr
ound in heterotic string theory is explicitly solved in terms of free
creation/annihilation operators. The spectrum of physical states is ex
amined for different possible embeddings of the magnetic U(1) subgroup
. We find that an arbitrarily small magnetic field gives rise to an in
finite number of tachyonic excitations corresponding to charged vector
states of the massless level and to higher level states with large sp
ins and charges.