We present 547 optical redshifts obtained for galaxies in the region of the Horologium-Reticulum supercluster (HRS) using the 6° field (6dF) multifiber spectrograph on the UK Schmidt Telescope at the Anglo-Australian Observatory. The HRS covers an area of more than 12deg×12deg on the sky centered at approximately α=03h19m, δ=-50deg02'. Our 6dF observations concentrate on the intercluster regions of the HRS, from which we describe four primary results. First, the HRS spans at least the redshift range from 17,000 to 22,500 km s-1. Second, the overdensity of galaxies in the intercluster regions of the HRS in this redshift range is estimated to be 2.4, or δρ/ρ̄~1.4. Third, we find a systematic trend of increasing redshift along a southeast-northwest spatial axis in the HRS, in that the mean redshift of HRS members increases by more than 1500 km s-1 from southeast to northwest over a 12° region. Fourth, the HRS is bimodal in redshift with a separation of ~2500 km s-1 (35 Mpc) between the higher and lower redshift peaks. This fact is particularly evident if the above spatial-redshift trend is fitted and removed. In short, the HRS appears to consist of two components in redshift space, each one exhibiting a similar systematic spatial-redshift trend along a southeast-northwest axis. Lastly, we compare these results from the HRS with the Shapley supercluster and find similar properties and large-scale features.