We propose a new chemical evolution model aimed at explaining the chemical properties of globular clusters (GC) 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 (SNeII), and (ii) localized inhomogeneous enrichment from a single Type Ia supernova (SNeIa) and intermediate-mass (4 7Msun) asymptotic giant branch (AGB) 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 SNeII occurs and the peculiar pollution from the previous phase is dispersed. In this study, we focus on three different GCs: NGC6752, NGC6205 (M13) and NGC2808. We demonstrate that, within this framework, a model can be constructed which is consistent with (i) the elemental abundance anti-correlations, (ii) isotopic abundance patterns, and (iii) the extreme [O/Fe] values observed in NGC2808 and M13, without violating the global constraints of approximately unimodal [Fe/H] and C+N+O.