We present high spectral resolution ( R \approx 108 , 000 ) Stokes V polarimetry of the Classical T Tauri stars ( CTTSs ) GQ Lup and TW Hya obtained with the polarimetric upgrade to the HARPS spectrometer on the ESO 3.6 m telescope . We present data on both photospheric lines and emission lines , concentrating our discussion on the polarization properties of the He i emission lines at 5876 Ã Â and 6678 Ã . The He i lines in these CTTSs contain both narrow emission cores , believed to come from near the accretion shock region on these stars , and broad emission components which may come from either a wind or the large scale magnetospheric accretion flow . We detect strong polarization in the narrow component of the two He i emission lines in both stars . We observe a maximum implied field strength of 6.05 \pm 0.24 kG in the 5876 Ã Â line of GQ Lup , making it the star with the highest field strength measured in this line for a CTTS . We find field strengths in the two He i lines that are consistent with each other , in contrast to what has been reported in the literature on at least one star . We do not detect any polarization in the broad component of the He i lines on these stars , strengthening the conclusion that they form over a substantially different volume relative the formation region of the narrow component of the He i lines .