We present the first unambiguous case of external variability of a radio gravitational lens, CLASS B1600+434. The VLA 8.5-GHz difference light curve of the lensed images, taking the proper time-delay into account, shows the presence of external variability with 14.6-sigma confidence. We investigate two plausible causes of this external variability: scattering by the ionized component of the Galactic interstellar medium and microlensing by massive compact objects in the bulge/disk and halo of the lens galaxy. Based on the tight relation between the modulation-index and variability time scale and the quantitative difference between the light curves of both lensed images, we conclude that the observed short-term variability characteristics of the lensed images are incompatible with scintillation in our Galaxy. This conclusion is strongly supported by multi-frequency WSRT observations at 1.4 and 5 GHz, which are in strong disagreement with predictions based on the scintillation hypothesis. ... On the other hand, a single superluminal jet-component, having an apparent velocity 9<=(v_app/c)<=26, a radius of 2-5 micro-arcsec and containing 5-11% of the observed 8.5-GHz source flux density, can reproduce the observed modulation-indices and variability time scale at 8.5 GHz, when it is microlensed by compact objects in the lens galaxy. It also reproduces the frequency-dependence of the modulation-indices, determined from the independent WSRT 1.4 and 5-GHz observations. ... The only conclusion fully consistent with the data gathered thus far is that we have indeed detected radio microlensing. The far reaching consequence of this statement is that a significant fraction of the mass in the dark-matter halo at ~6 kpc (h=0.65) above the lens-galaxy disk in B1600+434 consists of massive compact objects. [abridged]
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