  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 ($11
\leq z_{\rm f} \leq 30$) and assuming $\Omega_{\rm M} = 0.3 \pm 0.02$, 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 90.3% 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 $\Omega_{\rm M}$. The results show the high potential of the oldest stars
as independent and competitive cosmological probes not only limited to the
Hubble constant.
