Evidence is presented for redshift quantization in the Ly-alpha forest of several QSOs. The Ly-alpha data are at redshifts z from 1.89 to 3.74, and the theory of redshift quantization proposed by Cocke is used to scale the quantization interval (24.15 km/s) to these high redshifts. The scaling depends on the deceleration parameter q(0), and the quantization is present at a statistical significance of greater than 99 percent for q(0) = 1/2. This may be taken as confirming the inflationary model of the early history of the universe. The significance of the quantization is highest at q(0) approximately equal to 0.48, and the width of the peak is about 0.03. The result can also be seen as providing confirmatory evidence for both the theory of the redshift quantization and the above value of q(0), but at a significance of only 95 percent. The scenario proposed for the relativistic generalization of the theory is that of fermion wave functions and quantum operators in a background Riemannian spacetime satisfying Einstein’s field equations.