Negative-strand RNA viruses represent a significant class of important pathogens that cause substantial morbidity and mortality in human and animal hosts worldwide. A defining feature of these viruses is that their single-stranded RNA genomes are of opposite polarity to messenger RNA and are replicated through a positive-sense intermediate. The replicative intermediate is thought to exist as a complementary ribonucleoprotein (cRNP) complex. However, isolation of such complexes from infected cells has never been accomplished. Here we report the development of an RNA-based affinity-purification strategy for the isolation of cRNPs of influenza A virus from infected cells. This technological advance enabled the structural and functional characterization of this elusive but essential component of the viral RNA replication machine. The cRNP exhibits a filamentous double-helical organization with defined termini, containing the viral RNA-dependent RNA polymerase (RdRp) at one end and a loop structure at the other end. In vitro characterization of cRNP activity yielded mechanistic insights into the workings of this RNA synthesis machine. In particular, we found that cRNPs show activity in vitro only in the presence of added RdRp. Intriguingly, a replication-inactive RdRp mutant was also able to activate cRNP-templated viral RNA synthesis. We propose a model of influenza virus genome replication that relies on the trans-activation of the cRNP-associated RdRp. The described purification strategy should be applicable to other negative-strand RNA viruses and will promote studies into their replication mechanisms.