We present Far Ultraviolet Spectroscopic Explorer observations of interstel
lar molecular hydrogen (H-2) in two Galactic high-velocity clouds (HVCs). M
olecular hydrogen absorption is detected in the Magellanic Stream (abundanc
e similar to0.3 solar) toward the Seyfert galaxy Fairall 9 in the lowest th
ree rotational states (J = 0-2) at v(LSR) = +190 km s(-1), yielding a total
H-2 column density of log N(H-2) = 16.40(-0.53)(+0.26). In contrast, no H-
2 absorption is seen in the HVC Complex C (abundance similar to0.1 solar) t
oward the quasar PG 1259+593 [log N(H-2) less than or equal to 13.96 at v(L
SR) = -130 km s(-1)], although both HVCs have similar H I column densities
on the order of log N(H I) approximate to 20. Weak H-2 absorption is detect
ed in the Intermediate-Velocity Arch (IV Arch; abundance similar to1.0 sola
r) toward PG 1259+593 [log N(H-2) = 14.10(-0.44)(+0.21) at v(LSR) = -55 km
s(-1) and N(H I) = 19.5]. It thus appears that metal and dust-poor halo clo
uds like Complex C are not able to form and maintain widely distributed H-2
, whereas metal- and dust-rich halo clouds like the IV Arch can maintain H-
2 even at low H I column densities.