  Context. The chromospheric layer observable with the He I 10830 {\AA} triplet
is strongly warped. The analysis of the magnetic morphology of this layer
therefore requires a reliable technique to determine the height at which the He
I absorption takes place.
  Aims. The He I absorption signature connecting two pores of opposite polarity
in an emerging flux region is investigated. This signature is suggestive of a
loop system connecting the two pores. We aim to show that limits can be set on
the height of this chromospheric loop system.
  Methods. The increasing anisotropy in the illumination of a thin, magnetic
structure intensifies the linear polarization signal observed in the He I
triplet with height. This signal is altered by the Hanle effect. We apply an
inversion technique incorporating the joint action of the Hanle and Zeeman
effects, with the absorption layer height being one of the free parameters.
  Results. The observed linear polarization signal can be explained only if the
loop apex is higher than \approx5 Mm. Best agreement with the observations is
achieved for a height of 6.3 Mm.
  Conclusions. The strength of the linear polarization signal in the loop apex
is inconsistent with the assumption of a He I absorption layer at a constant
height level. The determined height supports the earlier conclusion that dark
He 10830 {\AA} filaments in emerging flux regions trace emerging loops.
