Cesium atoms in a vapor cell have been trapped and cooled by using light from laser diodes. The 6S F = 4, m = 0 --> 6S F = 3, m = 0 hyperfine clock transition was excited as these atoms then fell 2.5 cm in darkness. We observed a linewidth of 8 Hz with good signal-to-noise ratio. This gave a short-term fractional frequency resolution of 6.5 x 10(-12)/square-root-sec, and there is potential for substantial improvement. The apparatus is extremely simple and compact, consisting of a small cesium vapor cell and two diode lasers.