We report noble gas data for 37 H chondrites collected from the Allan Hills by EUROMET in the 1988-1989 field season. Among these are 16 specimens with high levels (>100 krad) of natural thermoluminescence (NTL), originally interpreted as signaling their derivation from a single meteoroid with an orbit that became Earth-crossing similar to 100 ka ago. One of these 16 is an H3 chondrite with a cosmic-ray exposure age of similar to 33 Ma and clearly represents a separate fall. The other 15 H4-6 chondrites derive from three separate meteoroids, each of which is represented by a five or six member group. These groups have mean exposure ages of 3.7, 4.1, and 6.6 Ma: the middle-group members all contain solar Ne. The two younger groups also seem to each include a few H chondrites with normal NTL levels. Measurements of cosmogenic Be-10 (1.5 Ma), Al-26 (710 ka), and Cl-36 (301 ka) in 14 of the high-NTL chondrites indicate that all reflect a simple irradiation history. In contrast, many of a different (38 member) randomly selected suite of Antarctic H chondrites seem to have different cosmic-ray irradiation histories. The 3.7 and 6.6 Ma groups from the 37 member Allan Hills suite come from about 5-30 and about 5-10 cm depths in 80-125 and 60-125 cm radius meteoroids, respectively.