  We present a new measurement of the s-wave scattering length a of
spin-polarized helium atoms in the 2^3S_1 metastable state. Using two-photon
photoassociation spectroscopy and dark resonances we measure the energy
E_{v=14}= -91.35 +/- 0.06 MHz of the least bound state v=14 in the interaction
potential of the two atoms. We deduce a value of a = 7.512 +/- 0.005 nm, which
is at least one hundred times more precise than the best previous
determinations and is in disagreement with some of them. This experiment also
demonstrates the possibility to create exotic molecules binding two metastable
atoms with a lifetime of the order of 1 microsecond.
