  We have obtained deep near-infrared images in J and K filters of three fields
in the Sculptor galaxy NGC 300 with the ESO VLT and ISAAC camera. For 16
Cepheid variables in these fields, we have determined J and K magnitudes at two
different epochs, and have derived their mean magnitudes in these bands. The
slopes of the resulting period-luminosity relations are in very good agreement
with the slopes of these relations measured in the LMC by Persson et al.
Fitting the LMC slopes to our data, we have derived distance moduli in J and K.
Using these values together with the values derived in the optical V and I
bands in our previous work, we have determined an improved total reddening for
NGC 300 of E(B-V)=0.096 +/- 0.006 mag, which yields extremely consistent values
for the absorption-corrected distance modulus of the galaxy from VIJK bands.
Our distance result for NGC 300 from this combined optical/near infrared
Cepheid study is (m-M)_0 = 26.37 +/- 0.04 (random) +/- 0.03 (systematic) mag
and is tied to an adopted true LMC distance modulus of 18.50 mag. Both random
and systematic uncertainties are dominated by photometric errors, while errors
due to reddening, metallicity effects and crowding are less important. Our
distance determination is consistent with the earlier result from near-infrared
(H-band) photometry of two Cepheids in NGC 300 by Madore et al., but far more
accurate. Our distance value also agrees with the HST Key Project result of
Freedman et al., and with the recent distance estimate for NGC 300 from Butler
et al. from the TRGB I-band magnitude when our improved reddening is used to
calculate the absorption corrections. Our distance results from the different
optical and near-infrared bands indicate that the reddening law in NGC 300 must
be very similar to the Galactic one.
