We study the surface magnetization of aperiodic Ising quantum chains.
Using fermion techniques, exact results are obtained in the critical r
egion for quasiperiodic sequences generated through an irrational numb
er as well as for the automatic binary Thue-Morse sequence and its gen
eralizations modulo p. The surface magnetization exponent keeps its Is
ing value, beta(s)=1/2, for all the sequences studied. The critical am
plitude of the surface magnetization depends on the strength of the mo
dulation and also on the starting point of the chain along the aperiod
ic sequence.