We report on observations of the J = 1-0 line of (CO)-C-12 at 115 GH,
toward several high-velocity H I clouds (HVCs). High angular resolutio
n observations at 21 cm show the presence of dense cores with N(H I) =
(2-4) x 10(20) cm(-2) and n(H I) = 30-800(kpc)(-1) cm(-3). We observe
d the CO line toward six of the densest HVC cores. No (CO)-C-12 emissi
on is detected down to a best 5 sigma limit of 0.077 K km s(-1). Using
the median I(CO) to N(H-2) conversion factor appropriate for high-lat
itude translucent clouds, this limit corresponds to a column density l
imit for N(H-2) of 9 x 10(18) cm(-2). We calculate the expected value
of N(H-2) assuming a standard formation mechanism for the molecules an
d accounting for the run of the interstellar radiation held with the a
ssumed distance to the HVC. The nondetections then indicate that the o
bserved HVCs are more distant than similar to 2 kpc. This is consisten
t with the results of interstellar absorption line studies, which yiel
d lower limits of 2-5 kpc for most of the observed HVCs. The nondetect
ions also suggest that HVC cores are not likely to be current sites of
star formation in the halo.