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We report evidence for the first generation of XUV spectra from relativisticsurface high-harmonic generation (SHHG) on plasma mirrors at a kilohertzrepetition rate, emitted simultaneously with energetic electrons. SHHG spectraand electron angular distributions are measured as a function of theexperimentally controlled plasma density gradient scale length $L_\mathrm{g}$for three increasingly short and intense driving pulses: 24~fs and $a_0=1.1$,8~fs and $a_0=1.6$, and finally 4~fs and $a_0\approx2.1$, where $a_0$ is thepeak vector potential normalized by $m_\mathrm{e} c/e$ with the elementarycharge $e$, the electron rest mass $m_\mathrm{e}$, and the vacuum lightvelocity $c$. For all driver pulses, we observe correlated relativistic SHHGand electron emission in the range $L_\mathrm{g}\in[\lambda/25,\lambda/5]$,with an optimum gradient scale length of $L_\mathrm{g}\approx\lambda/10$.

High-Harmonic Generation and Correlated Electron Emission from Relativistic Plasma Mirrors at 1 kHz Repetition Rate