We present new improved constraints on the Hubble parameter H(z) in the redshift range 0.15 < z < 1.1, obtained from the differential spectroscopic evolution of early-type galaxies as a function of redshift. We extract a large sample of early-type galaxies ( ~ 11000) from several spectroscopic surveys, spanning almost 8 billion years of cosmic lookback time (0.15 < z < 1.42). We select the most massive, red elliptical galaxies, passively evolving and without signature of ongoing star formation. Those galaxies can be used as standard cosmic chronometers, as firstly proposed by Jimenez & Loeb (2002), whose differential age evolution as a function of cosmic time directly probes H(z). We analyze the 4000 Å break (D4000) as a function of redshift, use stellar population synthesis models to theoretically calibrate the dependence of the differential age evolution on the differential D4000, and estimate the Hubble parameter taking into account both statistical and systematical errors. We provide 8 new measurements of H(z) (see table 4), and determine its change in H(z) to a precision of 5-12% mapping homogeneously the redshift range up to z ~ 1.1; for the first time, we place a constraint on H(z) at z≠0 with a precision comparable with the one achieved for the Hubble constant (about 5-6% at z ~ 0.2), and covered a redshift range (0.5 < z < 0.8) which is crucial to distinguish many different quintessence cosmologies. These measurements have been tested to best match a ΛCDM model, clearly providing a statistically robust indication that the Universe is undergoing an accelerated expansion. This method shows the potentiality to open a new avenue in constrain a variety of alternative cosmologies, especially when future surveys (e.g. Euclid) will open the possibility to extend it up to z ~ 2.