Amorphous transparent conductors (a-TCs) are key materials for flexible and transparent electronics but still suffer from poor p-type conductivity. By developing an amorphous Cu(S,I) material system, record high hole conductivities of 103-104 S cm-1 have been achieved in p-type a-TCs. These high conductivities are comparable with commercial n-type TCs made of indium tin oxide and are 100 times greater than any previously reported p-type a-TCs. Responsible for the high hole conduction is the overlap of large p-orbitals of I- and S2- anions, which provide a hole transport pathway insensitive to structural disorder. In addition, the bandgap of amorphous Cu(S,I) can be modulated from 2.6 to 2.9 eV by increasing the iodine content. These unique properties demonstrate that the Cu(S,I) system holds great potential as a promising p-type amorphous transparent electrode material for optoelectronics.