This pair was discovered on a U.K. Schmidt objective prism plate by C. Hazard and confirmed by Boksenberg and myself. Q2344+1229 has a magnitude of 17 and a redshift of z = 2.53, while Q2344+1225 has magnitude of 17.5 and a redshift of z = 2.77. There is a common absorption system in both objects at zabs = 2.42; in Q2344+1229 this system has a damped Ly- absorption line, while in Q2344+1225 the system is weaker and more complex. To add to the coincidences, there is a damped Ly- absorption in the higher redshift QSO, Q2344+1225, at zabs = 2.53, similar to that of the lower redshift object. The separation of these two QSOs is 5.7 arcmin, corresponding to 2 - 4 Mpc at z = 2.5, depending on the cosmological model. This is yet another case of a pair of common or associated absorption in relatively widely spaced QSOs. It will be interesting to explore the limits on the physical properties of the object responsible for the damped Ly- system in Q2344+1225 which are imposed by its proximity to Q2344+1229. Interestingly, there is a third, fainter QSO about 2 arcmin from Q2344+1225 with a similar emission redshift, z = 2.75, but with no common absorption systems.