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In this paper we consider a class of black holes in Einstein-Skyrme theory in even dimensional theories with negative cosmological constant Λ turned on. In addition, the Skyrme scalar field is chiral admitting a complex unitary group SU(2). We take some assumptions as follows. First, we simplify the spacetime to be conformal to a product space ( mathcal{M}^4 × mathcal{N}^{N−4} ) where (mathcal{M}^4) and ( mathcal{N}^{N−4} ) are a four dimensional spacetime and a compact Einstein ((N − 4))-dimensional submanifold with (N ≥ 4), respectively. Second, the representation of the group SU(2) is taken to be fundamental which means that we can use the (2 × 2) Pauli matrices in the theory. Third, the Skyrme field is static which depends only on the radial coordinate r. Then, we derive the Einstein field equation and the scalar equation of motions related to these setups. Our analysis shows that near boundaries, namely near horizon and around the asymptotic region, the geometries are of constant scalar curvature. To be precise, the near horizon geometry is a product space, whereas the geometry in the asymptotic limit is Einstein with negative cosmological constant. Finally, we perform Lipshitz localization method to show the local existence of solutions, and then, using the energy functional we show that finite energy solutions could exist.