RE J1034+396 has one of the hottest big blue bumps of any Seyfert 1 (kTBB∼120 eV) and thus provides a valuable insight into the physics in the nuclei of active galaxies. In this paper, we present UV spectroscopy of RE J1034+396, taken with the Faint Object Spectrograph on the Hubble Space Telescope. With a spectral resolution of ∼1–2 A FWHM and a typical signal-to-noise ratio of ∼15 per diode, this is one of the first detailed UV spectra of an object in the narrow-line Seyfert 1 (NLS1) class. The spectrum probes the physics and kinematics of the high-ionization and coronal line gas, and the strength and form of the big blue bump component in the UV. We detect many emission lines, including Lyα, C ivλ1549, He iiλ1640, C iii] λ1909 and Mg iiλ2798. We also identify a feature at 2647 A (in the rest frame) with highly ionized iron ([Fe xi] λ2649); a line of the same species ([Fe xi] λ7892) has also been seen in the optical spectrum. The velocity widths of the UV lines are relatively narrow (FWHM<2000 km s−1), although C ivλ1549 appears to have a broad underlying component with a FWHM typical of quasars (∼5500 km s−1). The FWHM are similar to those of the optical lines, which suggests that all line emission in RE J1034+396, i.e. including that of high- and low-ionization species and the forbidden lines, may be dominated by an intermediate-velocity (FWHM∼1000 km s−1), intermediate-density (log Ne ∼ 7.5 cm−3) region of gas. The slope of the UV continuum (αuv∼0.9) is soft (i.e. red) relative to quasars and the UV to soft X-ray flux ratio is unusually low (the 0.2 keV/1200 A flux ratio is 1/200), implying that the big blue bump component is very weak in the UV. The present-epoch UV to soft X-ray continuum is consistent with earlier data, demonstrating that this extreme big blue bump component is also very stable, unlike many other NLS1s which show extreme patterns of variability.