  Understanding how the electron spin is coupled to orbital degrees of freedom,
such as a valley degree of freedom in solid-state systems is central to
applications in spin-based electronics and quantum computation. Recent
developments in the preparation of electrostatically-confined quantum dots in
gapped bilayer graphene (BLG) enables to study the low-energy single-electron
spectra in BLG quantum dots, which is crucial for potential spin and
spin-valley qubit operations. Here, we present the observation of the
spin-valley coupling in a bilayer graphene quantum dot in the single-electron
regime. By making use of a highly-tunable double quantum dot device we achieve
an energy resolution allowing us to resolve the lifting of the fourfold spin
and valley degeneracy by a Kane-Mele type spin-orbit coupling of $\approx
65~\mu$eV. Also, we find an upper limit of a potentially disorder-induced
mixing of the $K$ and $K'$ states below $20~\mu$eV.
