We present a high-angular-resolution multi-wavelength study of the massive globular cluster NGC 1835 in the Large Magellanic Cloud. Thanks to a combination of optical and near-ultraviolet images acquired with the WFC3 on board the HST, we performed a detailed inspection of the stellar population in this stellar system, adopting a `UV-guided search' to optimize the detection of relatively hot stars. This allowed us to discover a remarkably extended horizontal branch (HB): it spans more than 4.5 magnitudes in both the optical and the near-ultraviolet bands, and its colour (temperature) ranges from the region redder than the instability strip up to effective temperatures of 30,000 K. This is the first time that such a feature has been detected in an extragalactic cluster, demonstrating that the physical conditions responsible for the formation of extended HBs are ubiquitous. The HB of NGC 1835 includes a remarkably large population of RR Lyrae (67 confirmed variables and 52 new candidates). The acquired dataset was also used to redetermine the cluster distance modulus, reddening, and absolute age: $(m-M)_0=18.58$, $E(B-V)=0.08$, and $t=12.5$ Gyr.