Negative ions (anions) were identified in the coma of comet 1P/Halley during in situ Electron Electrostatic Analyzer measurements performed by the Giotto spacecraft in 1986. These anions were detected with masses in the range 7–110 amu, but with insufficient mass resolution to permit unambiguous identification. We present details of a new chemical-hydrodynamic model for the coma of comet Halley that includes—for the first time—atomic and molecular anions, in addition to a comprehensive hydrocarbon chemistry. Anion number densities are calculated as a function of radius in the coma, and compared with the Giotto results. Important anion production mechanisms are found to include radiative electron attachment, polar photodissociation, dissociative electron attachment, and proton transfer. The polyyne anions C4H− and C6H− are found to be likely candidates to explain the Giotto anion mass spectrum in the range 49–73 amu. The CN− anion probably makes a significant contribution to the mass spectrum at 26 amu. Larger carbon-chain anions such as C8H− can explain the peak near 100 amu provided there is a source of large carbon-chain-bearing molecules from the cometary nucleus.