Models are presented for CO rotational line emission by high-redshift
starburst galaxies. The influence of the cosmic microwave background o
n the thermal balance and the level populations of atomic and molecula
r species is explicitly included. Predictions are made for tile observ
ability of starburst galaxies through line and continuum emission betw
een z = 5 and z = 30. It is found that the Millimeter Array could dete
ct a starburst galaxy with similar to 10(5) Orion regions, correspondi
ng to a star formation rate of about 30 M-. yr(-1), equally well at z
= 5 or z = 30 because of the increasing cosmic microwave background te
mperature with redshift. Line emission is a potentially more powerful
probe than dust continuum emission of very high redshift objects.