We have sympathetically cooled a small sample of 133Cs atoms with 87Rb to below 1 μK. Evaporative cooling was realized with microwave radiation driving the Rb ground-state hyperfine transition. By analysing the sympathetic cooling dynamics, we derive a lower limit of the modulus of the Rb–Cs interspecies triplet s-wave scattering length of 200 a_0. For temperatures below 5 μK we observe strong non-exponential losses of the Cs sample in the presence of the Rb sample.