  We report a uGMRT detection of HI 21-cm absorption associated with the radio
source 8C 0604+728, at $z = 3.52965$. The source is at the highest redshift at
which associated HI 21-cm absorption has been discovered to date, surpassing
earlier known absorber at $z \approx 3.39$. We estimate ultraviolet
luminosities of $\rm (3.2 \pm 0.1) \times 10^{23} W \ Hz^{-1}$ and $\rm (6.2
\pm 0.2) \times 10^{23} W \ Hz^{-1}$ , and ionising photon rates of $\rm (1.8
\pm 0.1) \times 10^{56} s^{-1}$ and $\rm (5.0 \pm 0.1) \times 10^{56} s^{-1}$,
using data at different epochs; the source shows year-scale variability in both
its luminosity and photon rate. The luminosity and photon rate at later epochs
are $\approx 6.2$ and $\approx 1.7$ times higher than thresholds suggested in
the literature above which all the neutral hydrogen in the AGN host galaxy is
expected to be ionised. The detection demonstrates that neutral hydrogen can
survive in the host galaxies of AGNs with high ultraviolet luminosities. We
estimate a high equivalent width ratio of $15.2$ for the $\rm Ly \alpha$ and
HeII emission lines detected in the optical spectrum, that is consistent with
AGN photoionisation models. However, a significant contribution from young
stellar populations to the excess $\rm Ly \alpha$ flux cannot be ruled out.
