We report a search for planetary nebulae and H II regions in the central part of the late-type spiral NGC 300, using a CCD and the on-band/off-band filter technique. The total exposure time for all frames was 4 hours. We have identified 34 PNs and 88 H II regions. We construct the cumulative [O III] {lambda}5007 PN luminosity function (PNLF) and obtain a distance modulus of 26.9+/-0.4, in satisfactory agreement with the Cepheid distance modulus (26.7+/-0.1). We make a general comparison between Cepheid and PNLF distances, showing that they are in excellent overall agreement. NGC 300 is in principle one of the best possible calibrators of the PNLF method of distance determination, to be preferentially applied, like the LMC, in cases of populations with recent star formation (as opposed to the bulge of M 31, which has served as calibrator for populations without recent star formation).