The generalized Chaplygin gas (GCG), with the equation of state p = -A/ρα, was recently proposed as a candidate for dark energy in the universe. In this paper we confront the GCG with Type Ia supernova (SN Ia) data using available samples. Specifically, we have tested the GCG cosmology in three different classes of models with (1) Ωm = 0.3 and ΩCh = 0.7, (2) Ωm = 0.05 and ΩCh = 0.95, and (3) Ωm = 0 and ΩCh = 1, as well as a model without prior assumptions on Ωm. The best-fit models are obtained by minimizing the χ2 function. We supplement our analysis with confidence intervals in the (A0, α)-plane by marginalizing the probability density functions (pdf's) over the remaining parameters assuming uniform priors. We have also derived one-dimensional pdf's for ΩCh obtained from joint marginalization over α and A0. The maximum value of such a pdf provides the most probable value of ΩCh within the full class of GCG models. The general conclusion is that SN Ia data give support to the Chaplygin gas (with α = 1). However, a noticeable preference for A0-values close to 1 means that the α dependence becomes insignificant. This is reflected in one-dimensional pdf's for α that turned out to be flat, meaning that the power of the present supernova data to discriminate between various GCG models (differing by α) is weak. Extending our analysis by relaxing the prior assumption of the flatness of the universe leads to the result that even though the best-fit values of Ωk are formally nonzero, they are still close to the flat case. Our results show clearly that in GCG cosmology, distant (i.e., z > 1) supernovae should be brighter than in the ΛCDM model. Therefore, one can expect that future supernova experiments (e.g., SNAP) having access to higher redshifts will eventually resolve the issue of whether the dark energy content of the universe could be described as a Chaplygin gas. Moreover, it would be possible to differentiate between models with various values of the α-parameter and/or discriminate between GCG, Cardassian, and ΛCDM models. This discriminative power of the forthcoming mission has been demonstrated on simulated SNAP data.