We report detailed measurements of low-frequency noise due to microwaves applied to a real Josephson tunnel junction. An intrinsically chaotic region is apparently identified, but the effects of thermal noise are shown to be significant. In particular we show experimental data that we interpret as evidence for thermally activated hopping and thermally affected chaos. The data are only in qualitative accord with recent ideas regarding the effect of thermal noise on intermittent chaos. © 1986 The American Physical Society.