Influenza A virus requires ongoing cellular transcription to carry out the cap-snatching process. Chromatin remodelers modify chromatin structure to produce an active or inactive conformation, which enables or prevents the recruitment of transcriptional complexes to specific genes; viral transcription thus depends on chromatin dynamics. Influenza virus polymerase associates with chromatin components of the infected cell, such as RNA polymerase II (RNAP II) or the CHD6 chromatin remodeler. Here we show that another CHD family member, CHD1 protein, also interacts with the influenza virus polymerase complex. CHD1 recognizes the H3K4me3 (histone 3 with a trimethyl group in lysine 4) histone modification, a hallmark of active chromatin. Downregulation of CHD1 causes a reduction in viral polymerase activity, viral RNA transcription, and the production of infectious particles. Despite the dependence of influenza virus on cellular transcription, RNAP II is degraded when viral transcription is complete, and recombinant viruses unable to degrade RNAP II show decreased pathogenicity in the murine model. We describe the CHD1-RNAP II association, as well as the parallel degradation of both proteins during infection with viruses showing full or reduced induction of degradation. The H3K4me3 histone mark also decreased during influenza virus infection, whereas a histone mark of inactive chromatin, H3K27me3, remained unchanged. Our results indicate that CHD1 is a positive regulator of influenza virus multiplication and suggest a role for chromatin remodeling in the control of the influenza virus life cycle. Although influenza virus is not integrated into the genome of the infected cell, it needs continuous cellular transcription to synthesize viral mRNA. This mechanism implies functional association with host genome expression and thus depends on chromatin dynamics. Influenza virus polymerase associates with transcription-related factors, such as RNA polymerase II, and with chromatin remodelers, such as CHD6. We identified the association of viral polymerase with another chromatin remodeler, the CHD1 protein, which positively modulated viral polymerase activity, viral RNA transcription, and virus multiplication. Once viral transcription is complete, RNAP II is degraded in infected cells, probably as a virus-induced mechanism to reduce the antiviral response. CHD1 associated with RNAP II and paralleled its degradation during infection with viruses that induce full or reduced degradation. These findings suggest that RNAP II degradation and CHD1 degradation cooperate to reduce the antiviral response.