Both CO and SiO have been observed at early and late phases in SN 1987A. H_2 was predicted to form at roughly the same time as these molecules, but was not detected at early epochs. Here we report the detection of NIR lines from H_2 at 2.12 mu and 2.40 mu in VLT/SINFONI spectra obtained between days 6489 and 10,120. The emission is concentrated to the core of the supernova in contrast to H-alpha and approximately coincides with the [Si I]/[Fe II] emission detected previously in the ejecta. Different excitation mechanisms and power sources of the emission are discussed. From the nearly constant H_2 luminosities we favour excitation resulting from the 44Ti decay.