Horizon shares Elevala-2 with Talisman Energy.
The well was spudded this week and was at 62m of its planned depth of 3500m yesterday afternoon.
Horizon aims to penetrate the Elevala sandstone and the deeper Toro sandstone about 2.1km west of the Elevala-1 discovery.
The well is located in Petroleum Retention Licence 21, which is owned by Horizon (45%), Talisman (40%) and Kina Petroleum (15%).
Kina Petroleum, which aims to float on the Australian Securities Exchange, also plans to transfer 5% of the licence to Talisman once the deal receives approval from PNG's petroleum and energy minister.