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.