We discuss the spectrum of excitons in quasi-one-dimensional crystals with strong orbital overlap between neighboring molecules. In such crystals, the energy difference between the lowest Frenkel exciton and charge-transfer exciton becomes small and their strong mixing determines the nature of the lowest energy states. We demonstrate here that in finite chains, simultaneously with excitonic 'bulk' states also 'surface' states can appear. The 'surface' states are localized at the end of the chain and can be blue- or red-shifted in comparison with the 'bulk' states. We discuss the contribution of these states to the absorption and fluorescence spectrum of molecular chains.