Young stars are thought to accumulate most of their mass through an accretion disk, which channels the gas and dust of a collapsing cloud onto the central protostellar object(1). The rotational and magnetic forces in the star-disk system often produce high-velocity jets of outflowing gas(2-6). These jets-an in principle be used to study the accretion and ejection history of the system, which is hidden from direct view by the dust and dense gas of the parent cloud. But the structures of these jets are often too complex to determine which features arise at the source and which are the result of subsequent interactions with, the surrounding gas. Here we present infrared observations of a very young jet driven by an invisible protostar in the vicinity of the Horsehead nebula in Orion. These observations reveal a sequence of geyser-like eruptions occurring at quasi-regular intervals and with near-perfect mirror symmetry either side of the source. This symmetry is strong evidence that such features must be associated with the formation of the jet, probably related to recurrent or even chaotic instabilities in the accretion disk.