  As supercomputers become larger with powerful Graphics Processing Unit (GPU),
traditional direct eigensolvers struggle to keep up with the hardware evolution
and scale efficiently due to communication and synchronization demands.
Conversely, subspace eigensolvers, like the Chebyshev Accelerated Subspace
Eigensolver (ChASE), have a simpler structure and can overcome communication
and synchronization bottlenecks. ChASE is a modern subspace eigensolver that
uses Chebyshev polynomials to accelerate the computation of extremal eigenpairs
of dense Hermitian eigenproblems. In this work we show how we have modified
ChASE by rethinking its memory layout, introducing a novel parallelization
scheme, switching to a more performing communication-avoiding algorithm for one
of its inner modules, and substituting the MPI library by the vendor-optimized
NCCL library. The resulting library can tackle dense problems with size up to
$N=\mathcal{O}(10^6)$, and scales effortlessly up to the full 900 nodes -- each
one powered by 4$\times$A100 NVIDIA GPUs -- of the JUWELS Booster hosted at the
J\"ulich Supercomputing Centre.
