We propose a new chemical evolution model aimed at explaining the chemical properties of globular clusters (GCs) stars. Our model depends upon the existence of (i) a peculiar pre-enrichment phase in the GC's parent galaxy associated with very low-metallicity Type II supernovae (SNe II) and (ii) localized inhomogeneous enrichment from a single Type Ia supernova (SN Ia) and intermediate-mass (4-7Msolar) asymptotic giant branch field stars. GC formation is then assumed to take place within this chemically peculiar region. Thus, in our model the first low-mass GC stars to form are those with peculiar abundances (i.e. O-depleted and Na-enhanced), while `normal' stars (i.e. O-rich and Na-depleted) are formed in a second stage when self-pollution from SNe II occurs and the peculiar pollution from the previous phase is dispersed. In this study, we focus on three different GCs: NGC 6752, 6205 (M 13) and 2808. We demonstrate that, within this framework, a model can be constructed which is consistent with (i) the elemental abundance anticorrelations, (ii) isotopic abundance patterns and (iii) the extreme [O/Fe] values observed in NGC 2808 and M 13, without violating the global constraints of approximately unimodal [Fe/H] and C+N+O.