  We present radio observations at three frequencies and contemporaneous
optical monitoring of the peculiar BL Lac object AO 0235+164. During a
three-week campaign with the VLA we observed intraday variability in this
source and found a distinct peak which can be identified throughout the radio
frequencies and tentatively connected to the R-band variations. This event is
characterized by unusual properties: its strength increases, and its duration
decreases with wavelength, and it peaks earlier at 20cm than at 3.6 and 6cm. We
discuss several generic models (a `standard' shock-in-jet model, a precessing
beam, free-free-absorption in a foreground screen, interstellar scattering, and
gravitational microlensing), and explore whether they can account for our
observations. Most attempts at explaining the data on 0235+164 require an
extremely small source size, which can be reconciled with the $10^{12}$ K
inverse Compton limit only when the Doppler factor of the bulk flow is of order
100. However, none of the models is completely satisfactory, and we suggest
that the observed variability is due to a superposition of intrinsic and
propagation effects.
