The remarkable astrometric capabilities of Chandra offer the possibility to measure proper motions of X-ray sources with an unprecedented accuracy in this wavelength range. We recently completed a proper motion survey of three of the seven thermally emitting radio-quiet isolated neutron stars (INSs) discovered in the ROSAT all-sky survey. These INSs (RX J0420.0-5022, RX J0806.4-4123, and RX J1308.6+2127) either lack an optical counterpart or have one so faint that ground based or space born optical observations push the current possibilities of the instrumentation to the limit. Pairs of ACIS observations were acquired 3 to 5 years apart to measure the displacement of the sources on the X-ray sky using as reference the background of extragalactic or remote Galactic X-ray sources. We derive 2 sigma upper limits of 123 mas/yr and 86 mas/yr on the proper motion of RX J0420.0-5022 and RX J0806.4-4123, respectively. RX J1308.6+2127 exhibits a very significant displacement (~ 9 sigma) yielding mu = 220 +/- 25 mas/yr, the second fastest measured among all ROSAT discovered INSs. The source is probably moving away rapidly from the Galactic plane at a speed which precludes any significant accretion of matter from the interstellar medium. Its transverse velocity of ~ 740 (d/700pc) km/s might be the largest of all ROSAT INSs and its corresponding spatial velocity stands among the fastest recorded for neutron stars. RX J1308.6+2127 is thus a middle-aged (age ~ 1 My) high velocity cooling neutron star. We investigate its possible origin in nearby OB associations or from a field OB star. In most cases, the flight time from birth place appears significantly shorter than the characteristic age derived from spin down rate. The distribution in transverse velocity of ROSAT INSs is not statistically different from that of normal radio pulsars.