  We show how to prepare a single molecular ion in a specific internal quantum
state in a situation where the molecule is trapped and sympathetically cooled
by an atomic ion and where its internal degrees of freedom are initially in
thermal equilibrium with the surroundings. The scheme is based on conditional
creation of correlation between the internal state of the molecule and the
translational state of the collective motion of the two ions, followed by a
projection measurement of this collective mode by atomic ion shelving
techniques. State preparation in a large number of internal states is possible.
