We describe a simple slow atom source for loading a rubidium magneto-optical trap. The source includes an effusive oven with a long heated collimation tube. Almost all components are standard vacuum parts. The heating elements and thermocouples are external to the vacuum, protecting them from the hostile hot alkali environment and allowing repair without breaking vacuum. The thermal source is followed by a Zeeman slower with a single-layer coil of variable winding pitch. The single-layer design is simple to construct and has low inductance which allows for rapid switching of the magnetic field. The coil pitch was determined by fitting the analytic form of the magnetic field for a variable winding pitch to the desired magnetic field profile required to slow atoms.