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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