We present a novel observation of the white-light flare (WLF) continuum, which was significantly enhanced during the X1 flare on March 29, 2014 (SOL2014-03-29T17:48). Data from the Interface Region Imaging Spectrograph (IRIS) in its NUV channel show that at the peak of the continuum enhancement, the contrast at the quasi-continuum window above 2813 \AA\ reached 100 - 200 % and can be even larger closer to the Mg II lines. This is fully consistent with the hydrogen recombination Balmer continuum emission, which follows an impulsive thermal and non-thermal ionization caused by the precipitation of electron beams through the chromosphere. However, a less probable photospheric continuum enhancement cannot be excluded. The light curves of the Balmer continuum have an impulsive character with a gradual fading, similar to those detected recently in the optical region on Hinode/SOT. This observation represents a first Balmer-continuum detection from space far beyond the Balmer limit (3646 \AA), eliminating seeing effects known to complicate the WLF detection. Moreover, we use a spectral window so far unexplored for flare studies, which provides the potential to study the Balmer continuum, as well as many metallic lines appearing in emission during flares. Combined with future ground-based observations of the continuum near the Balmer limit, we will be able to disentangle between various scenarios of the WLF origin. IRIS observations also provide a critical quantitative measure of the energy radiated in the Balmer continuum, which constrains various models of the energy transport and deposition during flares.