SignificanceThe large-scale circulation (LSC) is the key dynamical feature of turbulent thermal convection. It is the underlying structure that shapes the appearance of geo- and astrophysical systems, such as the solar granulation or cloud streets, and the cornerstone of theoretical models. Our laboratory-numerical experiments reveal that the LSC can perform a fully 3D motion resembling a twirling jump rope. The discovery of this LSC mode implies that the currently accepted paradigm of a quasi-planar oscillating LSC needs to be augmented. Moreover, it provides an important link between studies in confined geometries used in experiments and simulations and the effectively unconfined fluid layers in natural settings where an agglomeration of LSCs forms larger patterns.