Ventilation of the upper ocean plays an important role in climate variability on interannual to decadal timescales by influencing the exchange of heat and carbon dioxide between the atmosphere and ocean. The turbulent nature of ocean circulation, manifest in a vigorous mesoscale eddy field, means that pathways of ventilation, once thought to be quasi-laminar, are in fact highly chaotic. We characterize the chaotic nature of ventilation pathways according to a nondimensional filamentation number, which estimates the reduction in filament width of a ventilated fluid parcel due to mesoscale strain. In the subtropical North Atlantic of an eddy-permitting ocean model, the filamentation number is large everywhere across three upper ocean density surfaces-implying highly chaotic ventilation pathways-and increases with depth. By mapping surface ocean properties onto these density surfaces, we directly resolve the highly filamented structure and confirm that the filamentation number captures its spatial variability. These results have implications for the spreading of atmospherically-derived tracers into the ocean interior. Plain Language Summary When water leaves the surface ocean and spreads into the ocean interior, it carries with it climatically important properties that have been exchanged with the overlying atmosphere, such as heat and carbon dioxide. It is likely that a significant part of this ventilation process is achieved by relatively small-scale (around 50-100 km) eddying motions, which are ubiquitous in the turbulent ocean, but this remains poorly understood and difficult to quantify. By drawing an analogy with the making of puff pastry - in which the baker thins the layers of dough by repeated stretching and folding - we propose a novel way of quantifying the role of eddying motions in ventilation. We evaluate the extent to which the eddying motions (the baker) generate thin filaments in a fluid parcel (the dough) in the ocean interior. This, in turn, indicates whether pathways of water from the surface ocean into the ocean interior are straightforward or chaotic. In a numerical ocean simulation, we show that the latter is true - pathways are highly chaotic - supporting the case that eddying motions play an important role in the ventilation process.