A new Zintl phase Ba3Ga4Sb5 was obtained from the reaction of Ba and Sb in excess Ga flux at 1000°C, and its structure was determined with single-crystal X-ray diffraction methods. It crystallizes in the orthorhombic space group Pnma (No. 62) with a=13.248(3)Å, b=4.5085(9)Å, c=24.374(5)Å and Z=4. Ba 3Ga4Sb5 has a three-dimensional [Ga 4Sb5]6- framework featuring large tunnels running along the b-axis and accommodating the Ba ions. The structure also has small tube-like tunnels of pentagonal and rhombic cross-sections. The structure contains ethane-like dimeric Sb3Ga-GaSb3 units and GaSb4 tetrahedra that are connected to form 12- and 14-membered tunnels. Band structure calculations confirm that the material is a semiconductor and indicate that the structure is stabilized by strong Ga-Ga covalent bonding interactions.