High-order harmonic generation is a well-established process for producing coherent pulses in the soft-x-ray range by direct frequency conversion of femtosecond near-infrared pulses. Here, we show that a metallic bowtie-shaped gold nanoelement generates the extreme-ultraviolet pulses by means of plasmonic field enhancement. The intensity enhancement factor reaches a peak of ∼8100, allowing generation up to the 85th harmonic of a femtosecond Ti:sapphire laser  in hydrogen gas, with a modest incident intensity of ∼10¹¹ Wcm^–2.