On 2008 May 14, the Burst Alert Telescope onboard the Swift mission triggered on a type-I X-ray burst from the previously unclassified ROSAT object 1RXH J173523.7−354013, establishing the source as a neutron star X-ray binary. We report on X-ray, optical and near-infrared observations of this system. The X-ray burst had a duration of ∼2 h and belongs to the class of rare, intermediately long type-I X-ray bursts. From the bolometric peak flux of ∼3.5 × 10−8 erg cm−2 s−1, we infer a source distance of D≲ 9.5 kpc. Photometry of the field reveals an optical counterpart that declined from R= 15.9 during the X-ray burst to R= 18.9 thereafter. Analysis of post-burst Swift/X-ray Telescope observations as well as archival XMM–Newton and ROSAT data suggests that the system is persistent at a 0.5–10 keV luminosity of ∼2 × 1035 (D/9.5 kpc)2 erg s−1. Optical and infrared photometry together with the detection of a narrow Hα emission line (full width at half maximum = 292 ± 9 km s−1, equivalent width =−9.0 ± 0.4 Å) in the optical spectrum confirms that 1RXH J173523.7−354013 is a neutron star low-mass X-ray binary. The Hα emission demonstrates that the donor star is hydrogen rich, which effectively rules out that this system is an ultracompact X-ray binary.