We have confined over 5×1012 atoms of hydrogen in a static magnetic trap. The atoms are loaded into the trap by precooling with a dilution refrigerator. At operating densities near 1×1013 cm-3 the gas is observed to be electron- and nuclear-polarized in the uppermost hyperfine state. The long lifetime of the trapped gas (over 20 minutes) suggests that it is thermally decoupled from the wall and has evaporatively cooled to a temperature of about 41 mK. The residual decay of the gas density is consistent with spin relaxation induced by dipolar interactions between atoms.