The new ternary copper selenide NaCu4Se3 crystallizes in the RbCd4As3 structure type with the trigonal space group R3̅m and lattice constants a = 4.0316(4) Å and c = 31.438(8) Å. Its structure is built from two-dimensional slabs of (2)/∞[Cu4Se3] separated by Na(+) cations. The compound is formally mixed-valent with Se(2-)/Se(-) atoms and exhibits metallic properties. It is a hole conductor with an electrical conductivity of ∼300 S cm(-1) at room temperature and a thermopower of ∼10 μV K(-1). Hall effect measurements indicate holes as the dominant carrier with a concentration of ∼6.12(1) × 10(21) cm(-3) at 300 K. Density functional theory electronic structure calculations indicate p-type metallic behavior for the (2)/∞[Cu4Se3] framework, which is in a good agreement with the experimental metallic conductivity and Pauli paramagnetism.