Context. Siphon flows that are driven by a gas pressure difference between two photospheric footpoints of different magnetic field strength connected by magnetic field lines are a well-studied phenomenon in theory, but observational evidence is scarce. Aims. We investigate the properties of a structure in the solar chromosphere in an active region to find out whether the feature is consistent with a siphon flow in a magnetic loop filled with chromospheric material. Methods. We derived the line-of-sight (LOS) velocity of several photospheric spectral lines and two chromospheric spectral lines, Ca II H 3968.5 *Aring; and He I 10830 Å, in spectropolarimetric observations of NOAA 10978 done with the Tenerife Infrared Polarimeter (TIP-II) and the POlarimetric LIttrow Spectrograph (POLIS). The structure can be clearly traced in the LOS velocity maps and the absorption depth of He I. The magnetic field configuration in the photosphere is inferred directly from the observed Stokes parameters and from inversions with the HELIX+ code. Data from the full-disk Chromospheric Telescope (ChroTel) in He I in intensity and LOS velocity are used for tracking the temporal evolution of the flow, along with TRACE Fe IX/X 171 Å data for additional information about coronal regions related to the structure under investigation. Results. The inner end of the structure is located in the penumbra of a sunspot. It shows downflows whose strength decreases with decreasing height in the atmosphere. The flow velocity in He I falls abruptly from above 40 km s-1 to about zero further into the penumbra. A slight increase of emission is seen in the Ca II H spectra at the endpoint. At the outer end of the structure, the photospheric lines that form higher up in the atmosphere show upflows that accelerate with height. The polarization signal near the outer end shows a polarity opposite to that of the sunspot, the magnetic field strength of 580 G is roughly half as large as at the inner end. The structure exists for about 90 min. Its appearance is preceeded by a brightening in its middle in the coronal TRACE data. Conclusions. The observed flows match theoretical predictions of chromospheric and coronal siphon flows, with accelerating upflowing plasma at one footpoint with low field strength and decelerating downflowing plasma at the other end. A tube shock at the inner end is probable, but the evidence is not conclusive. The TRACE data suggest that the structure forms because of a reorganization of field lines after a reconnection event.