STUDIES of the formation and early history of galaxies have been hampered by the difficulties inherent in detecting faint galaxy populations at high redshift. As a consequence, observations at the highest redshifts (z = 3.5-5) have been restricted to objects that are Intrinsically bright, These include quasars, radio galaxies, and some Lyman-alpha-emitting objects(1-3) that are very close to (within similar to 10 kpc)-and appear to be physically associated with-quasars. But the extremely energetic processes which make these objects easy to detect also make them unrepresentative of normal (field) galaxies. Here we report the discovery of two Lyntan-alpha-emitting galaxies at redshift z = 4.55, which are sufficiently far from the nearest quasar (similar to 700 kpc) that radiation from the quasar is unlikely to provide the excitation source of the Lyman-alpha emission. Instead, these galaxies appear to be undergoing their first burst of star formation, at a time when the Universe was less than one billion years old.