We present a detection of [CI] line emission in the lensed quasar APM 08279+5255 at z=3.91 using the IRAM Plateau de Bure interferometer. The [CI] line velocity and width are similar to the values of previously detected high-J CO and HCN lines in this source, suggesting that the emission from all of these species arises from the same region. The apparent luminosity of the [CI] line is L(CI) = (3.1 +/- 0.4)x10^10 K km/s pc^2, which implies a neutral carbon mass, M(CI) = (4.4+/-0.6)/m x10^7 M_sun, where m is the lensing magnification factor. The [CI] line luminosity is consistent with the large molecular gas mass inferred from the nuclear CO line luminosity ~10^11 /m M_sun. We also present an upper limit on the H2O line luminosity in APM 08279+5255 of, L(H2O) < 1.8x10^10 K km/s pc^2 (3-sigma).