Despite a wide array of applications, deep ultra-violet light emitting diodes offer relatively poor efficiencies compared to their optical counterparts. A contributing factor is the lower light extraction efficiency due to both highly absorbing p-contacts and total internal reflection. Here, we propose a structure consisting of a hexagonal periodic array of cylindrical nanoholes in the multi-layered p-contact which are filled with platinum. This nanostructure reduces the absorption of the p-contact layer, leading to a higher emission into the n-contact compared to a planar reference. An optimum geometry of the nanostructure allows a light extraction efficiency of 15.0%, much higher than the typical 4.6% of a planar reference. While the nanostructure strongly decreases the light absorption in the p-contact, it is still not able to considerably reduce the total internal reflection. Consequently, the nanostructured p-contact should be combined with other optical strategies, such as nanopatterned sapphire substrates to increase the efficiency even further. Despite this, the nanostructure described in this work provides a readily realizable path to enhancing the light extraction efficiency of state-of-the-art deep ultra-violet light emitting diodes.