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MAXI J1305-704 has been proposed as a high-inclination candidate black holeX-ray binary in view of its X-ray properties and dipping behaviour duringoutburst. We present photometric and spectroscopic observations of the sourcein quiescence that allow us to reveal the ellipsoidal modulation of thecompanion star and absorption features consistent with those of an early K-typestar (Teff = 4610 +130 -160 K). The central wavelengths of the absorption linesvary periodically at Porb = 0.394 +- 0.004 d with an amplitude of K2 = 554 +- 8km/s . They imply a mass function for the compact object of f(M1) = 6.9 +- 0.3Msun, confirming its black hole nature. The simultaneous absence of X-rayeclipses and the presence of dips set a conservative range of allowedinclinations 60 deg < i < 82 deg, while modelling of optical light curvesfurther constrain it to i = 72 +5 -8 deg. The above parameters together set ablack hole mass of M1 = 8.9 +1.6 -1.0 Msun and a companion mass of M2=0.43 +-0.16 Msun, much lower than that of a dwarf star of the observed spectral type,implying it is evolved. Estimates of the distance to the system (d = 7.5 +1.8-1.4 kpc) and space velocity (vspace = 270 +- 60 km/s ) place it in theGalactic thick disc and favour a significant natal kick during the formation ofthe BH if the supernova occurred in the Galactic Plane.

Dynamical confirmation of a stellar-mass black hole in the transient X-ray dipping binary MAXI J1305-704