  We discuss the consequences of Lorentz violation (as expressed within the
Lorentz-violating extension of the standard model) for the hydrogen molecule,
which represents a generic model of a molecular binding. Lorentz-violating
shifts of electronic, vibrational and rotational energy levels, and of the
internuclear distance are calculated. This offers the possibility of obtaining
improved bounds on Lorentz invariance by experiments using molecules.
