We test a method of estimating the power spectrum of turbulence in molecular clouds based on the comparison of power spectra of integrated intensity maps and single-velocity-channel maps , suggested by Lazarian and Pogosyan . We use synthetic ^ { 13 } CO data from non-LTE radiative transfer calculations based on density and velocity fields of a simulation of supersonic hydrodynamic turbulence . We find that the method yields the correct power spectrum with good accuracy . We then apply the method to the Five College Radio Astronomy Observatory ^ { 13 } CO map of the Perseus region , from the COMPLETE website . We find a power law power spectrum with slope \beta = 1.81 \pm 0.10 . The values of \beta as a function of velocity resolution are also confirmed using the lower resolution map of the same region obtained with the AT & T Bell Laboratories antenna . Because of its small uncertainty , this result provides a useful constraint for numerical codes used to simulate molecular cloud turbulence .