Despite the tremendous advance of observational cosmology, the value of the Hubble constant (H 0 ) is still controversial (the so called "Hubble tension") because of the inconsistency between local/late-time measurements and those derived from the cosmic microwave background. As the age of the Universe is very sensitive to H 0 , we explored whether the present-day oldest stars could place independent constraints on the Hubble constant. To this purpose, we selected from the literature the oldest objects (globular clusters, stars, white dwarfs, ultra-faint and dwarf spheroidal galaxies) with accurate age estimates. Adopting a conservative prior on their formation redshifts (11 ≤ z f ≤ 30) and assuming Ω M = 0.3 ± 0.02, we developed a method based on Bayesian statistics to estimate the Hubble constant. We selected the oldest objects (> 13.3 Gyr), and estimated H 0 both for each of them individually and for the average ages of homogeneous subsamples. Statistical and systematic uncertainties were properly taken into account. The constraints based on individual ages indicate that H 0 < 70.6 km/s/Mpc when selecting the most accurate estimates. If the ages are averaged and analyzed independently for each subsample, the most stringent constraints imply H 0 < 73.0 with a probability of 93.2% and errors around 2.5 km/s/Mpc. We also constructed an "accuracy matrix" to assess how the constraints on H 0 become more stringent with further improvements in the accuracy of stellar ages and Ω M . The results show the high potential of the oldest stars as independent and competitive cosmological probes.