We study the dependence of the location of the Cosmic Microwave Background Radiation ( CMBR ) peaks on the parameters of the generalized Chaplygin gas model , whose equation of state is given by p = - A / \rho ^ { \alpha } , where A is a positive constant and 0 < \alpha \leq 1 . We find , in particular , that observational data arising from Archeops for the location of the first peak , BOOMERANG for the location of the third peak , supernova and high-redshift observations allow constraining significantly the parameter space of the model . Our analysis indicates that the emerging model is clearly distinguishable from the \alpha = 1 Chaplygin case and the \Lambda CDM model .