The histone chaperone SET is required for transcription of chromatin templates by RNA polymerase Pol II (Pol II) in vitro. Here we uncover a positive role for SET in dislodging DEK and PARP1, which restrict access to chromatin in the absence of SET and the PARP1 substrate NAD(+). SET binds chromatin, dissociating DEK and PARP1 to allow transcription in the absence of NAD(+). In the absence of SET, depletion of DEK restores chromatin accessibility to endonuclease but does not permit Mediator recruitment or transcription. In the presence of NAD(+), PARP1 poly(ADP-ribosyl)ates and evicts DEK (and itself) from chromatin to permit Mediator loading and transcription independent of SET. An artificial DEK variant resistant to SET and PARP1 represses transcription, indicating a requirement for DEK removal. Therefore, SET, DEK and PARP1 constitute a network governing access to chromatin by the transcription machinery.