We report evidence for the first generation of XUV spectra from relativistic surface high-harmonic generation (SHHG) on plasma mirrors at a kilohertz repetition rate, emitted simultaneously and correlated to the emission of energetic electrons. We present measurements of SHHG spectra and electron angular distributions as a function of the experimentally controlled plasma density gradient scale length L for three increasingly short and intense driving pulses: 24 fs (9 optical cycles) and a0 = 1.1, 9 fs (3.5 optical cycles) and a0 = 1.8, and finally 4 fs (1.7 optical cycles) and a0 ≈ 2.0. For all driver pulses, we observe relativistic SHHG in the range L ∈ [λ/25, λ/10], with an optimum gradient scale length of L ≈ λ/15. Surface high-harmonic generation (SHHG) [1] from relativistic plasma mirrors is a promising method for greatly enhancing the available energy of attosecond XUV pulses. This is motivated by the absence of an inherent limitation for the driving intensity such that extremely large numbers of photons from ultra-high intensity lasers can can be converted into attosecond XUV pulses. In strongly relativistic conditions with a normalized vector potential a 0 = I[W cm −2 ] λ 2 0 [µm 2 ]/(1.37 × 10 18) 1, where I is the laser intensity and λ 0 the central wavelength, this is expected to occur with extremely high, percent-level conversion efficiencies [2-4]. Reported experimentally observed laser-to-XUV conversion efficiencies for plasma mirrors with a 0 ∼ 1 are ∼ 10 −4 [5-8], but are expected to increase with higher-intensity drivers. Reaching relativistic SHHG regime with a 0 > 1 requires an on-target intensity of > ∼ 10 18 W/cm 2 for an 800-nm laser while retaining a very steep surface plasma density profile, i.e. a profile n(x) = n c exp [x/ L], with a scale length L of a small fraction of the diving laser wavelength. Here n c is the nonrelativstic critical plasma density for the driving wavelength and x is the coordinate in the target normal direction. Technically this requires a highly focusable terawatt-class driver laser with a temporal contrast of > ∼ 10 10. These conditions are typically met by Joule-class amplifier chains with dedicated contrast filters [9, 10] and operating at ∼ 10 Hz repetition rate [4-9]. Many applications as well as parametric studies of this regime would benefit from a higher repetition rate. At LOA, we have developed a unique laser chain with power-scaled hollow-core-fiber postcompression system [11] operating at 1 kHz repetition rate. Using this kHz-laser, which achieves ultra-high intensties with few-mJ pulse energy and few-cycle pulse duration, we have demonstrated laser-plasma interaction in the relativistic regime through laser-wakefield acceleration of electrons both in under-dense gas jets [11, 12] and in the underdense part of a smooth plasma density gradient on a plasma mirror [13]. Here we report on the first experimental demonstration of relativistic SHHG at kHz-repetition rate, the arguably most demanding application in terms of laser performance as it depends critically on the spatio-temporal pulse quality and the temporal contrast. For relativistic driving intensities, a 0 > ∼ 1, the SHHG emission mechanism is described by a push-pull process [14], also dubbed "relativistic electron spring" [15, 16], repeating once per driving laser period. The incident laser field first pushes electrons into the plasma, piling up a dense electron bunch and creating a restoring internal plasma field. As the laser field changes sign, the combined plasma and laser fields accelerate the electron bunch to a relativistic velocity towards the vacuum. SHHG