Poliovirus (PV), a model for interactions of picornaviruses with host cells, replicates its genomic RNA in association with cellular membranes. The origin of PV replication membranes has not been determined. Hypotheses about the origin of replication membranes, based largely on localization of viral proteins, include modification of coat protein complex I (COPI) and/or COPII secretory pathway vesicles and subversion of autophagic membranes. Here, we use an antibody against double-stranded RNA (dsRNA) to identify replication complexes by detection of dsRNA replication intermediates. dsRNA signal is dependent on virus genome replication and colocalizes with the viral integral membrane protein 3A, which is part of the RNA replication complex. We show that early in infection, dsRNA does not colocalize with a marker for autophagic vesicles, making it unlikely that autophagosomes contribute to the generation of PV RNA replication membranes. We also find that dsRNA does not colocalize with a marker of the COPII coat, Sec31, and, in fact, we demonstrate proteasome-dependent loss of full-length Sec31 during PV infection. These data indicate that COPII vesicles are an unlikely source of PV replication membranes. We show that the Golgi resident G-protein Arf1 and its associated guanine nucleotide exchange factor (GEF), GBF1, transiently colocalize with dsRNA early in infection. In uninfected cells, Arf1 nucleates COPI coat formation, although during infection the COPI coat itself does not colocalize with dsRNA. Phosphatidylinositol-4-phosphate, which is associated with enterovirus-induced vesicles, tightly colocalizes with Arf1/GBF1 throughout infection. Our data point to a noncanonical role for some of the COPI-generating machinery in producing unique replication surfaces for PV RNA replication. IMPORTANCE Picornaviruses are a diverse and major cause of human disease, and their genomes replicate in association with intracellular membranes. There are multiple hypotheses to explain the nature and origin of these membranes, and a complete understanding of the host requirements for membrane rearrangement would provide novel drug targets essential for viral genome replication. Here, we study the model picornavirus, poliovirus, and show that some, but not all, components of the cellular machinery required for retrograde traffic from the Golgi apparatus to the endoplasmic reticulum are transiently present at the sites of viral RNA replication. We also show that the full-length Sec31 protein, which has been suggested to be present on PV RNA replication membranes, is lost during infection in a proteasome-dependent manner. This study helps to reconcile multiple hypotheses about the origin of poliovirus replication membranes and points to known host cell protein complexes that would make likely drug targets to inhibit picornavirus infections.