SWAS and Odin provided stringent upper limits on the gas phase water abundance of dark clouds (x(H2O) < 7x10^-9). We investigate the chemistry of water vapor in starless cores beyond the previous upper limits using the highly improved angular resolution and sensitivity of Herschel and measure the abundance of water vapor during evolutionary stages just preceding star formation. High spectral resolution observations of the fundamental ortho water (o-H2O) transition (557 GHz) were carried out with Herschel HIFI toward two starless cores: B68, a Bok globule, and L1544, a prestellar core embedded in the Taurus molecular cloud complex. The rms in the brightness temperature measured for the B68 and L1544 spectra is 2.0 and 2.2 mK, respectively, in a velocity bin of 0.59 km s^-1. The continuum level is 3.5+/-0.2 mK in B68 and 11.4+/-0.4 mK in L1544. No significant feature is detected in B68 and the 3 sigma upper limit is consistent with a column density of o-H2O N(o-H2O) < 2.5x10^13 cm^-2, or a fractional abundance x(o-H2O) < 1.3x10^-9, more than an order of magnitude lower than the SWAS upper limit on this source. The L1544 spectrum shows an absorption feature at a 5 sigma level from which we obtain the first value of the o-H2O column density ever measured in dark clouds: N(o-H2O) = (8+/-4)x10^12 cm^-2. The corresponding fractional abundance is x(o-H2O) ~ 5x10^-9 at radii > 7000 AU and ~2x10^-10 toward the center. The radiative transfer analysis shows that this is consistent with a x(o-H2O) profile peaking at ~10^-8, 0.1 pc away from the core center, where both freeze-out and photodissociation are negligible. Herschel has provided the first measurement of water vapor in dark regions. Prestellar cores such as L1544 (with their high central densities, strong continuum, and large envelopes) are very promising tools to finally shed light on the solid/vapor balance of water in molecular clouds.Read less <