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We derive a new constraint on the expansion history of the Universe byapplying the cosmic chronometers method, studying the age evolution ofhigh-redshift galaxies with a full-spectral-fitting approach. We select asample of 39 massive ($log(M/M_\odot)>10.8$) and passive($log(sSFR/yr^{-1})<-11$) galaxies from the data release 4 of the VANDELSsurvey at $1<z<1.5$, combining different selection criteria to minimize thepotential contamination by star-forming outliers. We performfull-spectral-fitting jointly on spectra and photometry of our sources with thecode BAGPIPES, without any cosmological assumption on the age of thepopulation. The derived physical properties of the selected galaxies arecharacteristic of a passive population, with short star formation timescales($<\tau>=0.28\pm0.02$ Gyr), low dust extinction ($<A_{V,dust}>=0.43\pm0.02$mag), and sub-solar metallicities ($<Z/Z_{\odot}>=0.44\pm0.01$). The ages showa decreasing trend with redshift compatible with a standard cosmological model,even if no cosmological constraint is assumed in the fit, and a clearmass-downsizing pattern. Testing the impact of the star formation history onthe results, we find only a maximum 2\% fluctuation in age and metallicity. Byfitting the median age-redshift relation with a flat $\Lambda$CDM model andassuming a Gaussian prior on $\Omega_{M,0}= 0.3\pm0.02$ from late-Universeprobes, we obtain $H_0=67_{-15}^{+14}\:km\:s^{-1}\:Mpc^{-1}$. In the end, wederive a new estimate of the Hubble parameter with the cosmic chronometersmethod, $H(z=1.26)=135\pm65\:km\:s^{-1}\:Mpc^{-1}$ including statistical andsystematic errors. While the error budget is currently dominated by thescarcity of the sample, this work proves the potential strength of the cosmicchronometers approach up to $z>1$, especially in view of incoming largespectroscopic surveys like Euclid. (abridged)

A new measurement of the expansion history of the Universe at z=1.26 with cosmic chronometers in VANDELS