We report the first detection of molecular gas beyond redshift 7. The molecular gas is associated with the host galaxy of the quasar candidate PSO J145.5964+19.3565 and its companion PSO J145.5964+19.3565N separated by 20.7 kpc. The molecular gas of both companions is detected in two rotational transition lines of carbon monoxide, CO(6-5) and CO(7-6), with total luminosities of LCO 6-5 > 26′ 10 8 ( ) and LCO 7-6 > 17′ 10 8 ( ) Le. The two companions contain (36-54) × 1010Me of molecular gas assuming that their CO spectral line energy distributions are typical for star-forming galaxies. We also detected the Lyα line of PSO J145.5964+19.3565 at z ≈ 7.08. The Lyα line emission is extended and might represent the blended emission of two different sources at a separation of <5 kpc. The detected CO and Lyα emission likely originate from a system of interacting star-forming galaxies that might host a quasar(s). We also report the detection of a new emission line from the system that is a possible 793.62-GHz water maser line.