Amyloid fibrils are affiliated with various human pathologies. Knowledge of their molecular architecture is necessary for a detailed understanding of the mechanism of fibril formation. Vibrational circular dichroism (VCD) spectroscopy has recently shown sensitivity to amyloid fibrils [Ma et al. J. Am. Chem. Soc. 2007, 129, 12364 and Measey et al. J. Am. Chem. Soc. 2009, 131, 18218]. In particular, amyloid fibrils give rise to an intensity enhanced signal in the amide I band region of the corresponding VCD spectrum, offering promise of utilizing such a method for probing fibrillogenesis and the chiral structure of fibrils. Herein, we further investigate this phenomenon and demonstrate the use of VCD to probe the fibril formation kinetics of a short alanine-rich peptide. To elucidate the origin of the anomalous VCD intensity enhancement, we use an excitonic coupling model to simulate the VCD spectrum of stacked beta-sheets containing one (Ising-like model) and two amide I oscillators per strand, as models for the underlying amyloid-fibril secondary structure. With this simple model, we show that the VCD intensity enhancement of amyloid-like fibrils results from intrasheet and, to a more limited extent, also from intersheet vibrational coupling between stacked beta-sheets. The enhancement requires helically twisted sheets and is most pronounced for arrangements with parallel-oriented strands. Both the intersheet distance and the orientation of the amide I transition dipole moments of neighboring sheets are found to modulate the intensity enhancement of the amide I VCD signal. Moreover, our simulations suggest that, depending on the three-dimensional arrangement of the beta-strands, the sign of the VCD signal of amyloid-like fibrils can be used to distinguish between right- and left-handed helical twists of parallel-oriented beta-sheets. We compare the results of our simulation to experimental spectra of two short peptides, GNNQQNY, the N-terminal peptide fragment of the yeast prion protein Sup3S, and an amyloidogenic alanine-rich peptide, AKY8. Our results demonstrate the advantages of using VCD spectroscopy to probe the kinetics of peptide and protein aggregation as well as the chirality of the resulting supramolecular structure.