We report an efficient Cu Kα x-ray source produced by focusing submillijoule, 120 fs Ti:sapphire laser pulses on a solid copper target to a spot diameter of few microns. The experimental results show strong emission of Kα x-rays from solid targets from microplasmas created by p-polarized 0.2–0.3 mJ laser pulses at 1 kHz repetition rate. We have demonstrated Kα x-ray point source emission rates of 6.7×109 photons/s into 2π sr at 1 kHz repetition rate. The source has an x-ray conversion efficiency into Cu Kα line emission of 3.2×10-5. The source has a measured size of ∼8 μm. Such a high repetition rate Kα x-ray source can be very useful for time resolved x-ray diffraction and radiographic applications.