NGC 3147 has been considered the best case of a true type 2 AGN: an unobscured AGN, based on the unabsorbed compact X-ray continuum, which lacks a broad-line region (BI,R). However, the very low luminosity of NGC 3147 implies a compact BLR, which produces very broad lines, hard to detect against the dominant background host galaxy. Narrow (0.1 arcsec x 0.1 arcsec) slit HST spectroscopy allowed us to exclude most of the host galaxy light, and revealed an H alpha line with an extremely broad base (FWZI similar to 27 000 km s(-1)). The line profile shows a steep cut-off blue wing and an extended red wing, which match the signature of a mildly relativistic thin accretion disc line profile. It is indeed well fit with a nearly face on thin disc, at i similar to 23 degrees, with an inner radius at 77 +/- 15 r(g), which matches the prediction of 62(-14)(+18)r(g) from the R-BLR-L-1/2 relation. This result questions the very existence of true type 2 AGN. Moreover, the detection of a thin disc, which extends below 100 r(g) in an L/L-Edd similar to 10(-4) system, contradicts the current view of the accretion flow configuration at extremely low accretion rates.