L1457 is the closest known molecular cloud (65 pc), and it lies near t
he edge of the local hot bubble and well out of the Galactic plane (b
similar to -34 degrees). We have mapped an 8 degrees x 8 degrees regio
n at 35' resolution and a 3 degrees x 5 degrees region at similar to 2
' resolution in H I 21 cm emission. We have also mapped a 2 degrees x
4 degrees region at 2' resolution in (CO)-C-12 J = 1-0. We find that t
here is an extended component of atomic gas, clearly associated with t
he molecular complex and comparable to it in total mass. The H I struc
ture at small scales in the vicinity of the molecular clouds is remark
able, consisting largely of long, narrow filaments less than 20' (0.2
pc) in width and 1 degrees-4 degrees in length. A thin (<10') limb-bri
ghtened atomic halo is seen to surround the CO at some velocities, but
it is ill-defined at other velocities. The halo may be disturbed by e
xternal pressure, perhaps from the hot gas in the local bubble. The mo
lecular clouds are part of a large structure similar to 5 degrees x 3
degrees in extent with a small ''funnel-shaped'' extension to the sout
h. The structure, which we call the L1457 atomic/molecular complex, is
dominated by H I in the north and H, in the south extension. Roughly
one-half the mass of the complex is molecular. The structure of this c
omplex at both large- and small-scale suggests that the south end has
been recently compressed.