We show that two-photon absorption (TPA) in rubidium atoms can be greatly enhanced by the use of a hollow-core photonic-band-gap fiber. We investigate off-resonant, degenerate Doppler-free TPA on the $5{S}_{1/2}\ensuremath{\rightarrow}5{D}_{5/2}$ transition and observe
1 absorption of a pump beam with a total power of only 1 mW in the fiber. These results are verified by measuring the amount of emitted blue fluorescence and are consistent with the theoretical predictions which indicate that transit-time effects play an important role in determining the two-photon absorption cross section in a confined geometry.