  We report photon-noise limited performance of horn-coupled, aluminum
lumped-element kinetic inductance detectors at millimeter wavelengths. The
detectors are illuminated by a millimeter-wave source that uses an active
multiplier chain to produce radiation between 140 and 160 GHz. We feed the
multiplier with either amplified broadband noise or a continuous-wave tone from
a microwave signal generator. We demonstrate that the detector response over a
40 dB range of source power is well-described by a simple model that considers
the number of quasiparticles. The detector noise-equivalent power (NEP) is
dominated by photon noise when the absorbed power is greater than approximately
1 pW, which corresponds to $\mathrm{NEP} \approx 2 \times 10^{-17} \,
\mathrm{W} \, \mathrm{Hz}^{-1/2}$, referenced to absorbed power. At higher
source power levels we observe the relationships between noise and power
expected from the photon statistics of the source signal: $\mathrm{NEP} \propto
P$ for broadband (chaotic) illumination and $\mathrm{NEP} \propto P^{1/2}$ for
continuous-wave (coherent) illumination.
