The domain boundaries in a monolayer of fatty acids absorbed onto a graphite substrate were directly observed using a scanning tunneling microscope (STM). For all the fatty acids observed, the STM images of the monolayers were composed of bright bands corresponding to the alkyl chains and dark regions at the carboxyl groups via hydrogen bonding. There are three configuration of domains in the monolayers according to the three main crystallographic axes of the graphite substrate, i.e. the directions of the bright bands in neighboring domains make an angle of 120 degrees with each other at the domain boundaries. A variety of the images was obtained at the domain boundaries, such as bright and noisy regions and dark regions corresponding to free volume. The motion of the domain boundaries were often detected between two successive STM images over several tens of seconds. Molecular rearrangements in small domains were also observed during scanning. These facts indicate the existence of molecular motion on the graphite substrate.