Chlorine-enhanced GaAs maskless etching using a novel focused-ion-beametching (FIBE) system has been examined for establishing high-rate and smooth FIBE. The system is composed of an air-locked ultrahigh-vacuum chamber, a 30 KeV Ga+ FIB column and two kinds of chlorine-irradiation nozzles. A fine nozzle enabled us to irradiate a high-density Cl2 flux on a desired, small area of the sample while retaining a sufficiently low surrounding-gas pressure for stable Ga+ FIB emission. Highly chemically-enhanced sputtering yields (up to 50 GaAs molecules per incident ion) were obtained. At the maximum yield, line-scanned deep-groove (6.5 um) etching with a smooth surface, capable of fabricating a laser-cavity optical mirror, was demonstrated. The chemical-enhancement effect showed high FIB-scanning-time dependence. This effect was also observed by irradiating with a plasma-dissociated Cl radicals using a novel radical beam gun. An analytical model, based on the Ga+-ion bombardment on the chlorine-adsorbed substrate surface, suggested that the maximum chemical enhancement is obtained when the Ga+-FIB scanning time is adjusted to the chlorine-coverage time, given by the Cl2-molecule or Cl-radical flux density.