High-spatial resolution near-infrared (NIR) images of the central 24 x 24 arcsec^2 (~ 2 x 2 kpc^2) of the elliptical galaxy NGC 1052 reveal a total of 25 compact sources randomly distributed in the region. Fifteen of them exhibit Halpha luminosities an order of magnitude above the estimate for an evolved population of extreme horizontal branch stars. Their Halpha equivalent widths and optical-to-NIR spectral energy distributions are consistent with them being young stellar clusters aged < 7 Myr. We consider this to be the first direct observation of spatially resolved star-forming regions in the central kiloparsecs of an elliptical galaxy. The sizes of these regions are ~< 11 pc and their median reddening is E(B - V) ~ 1 mag. According to previous works, NGC 1052 may have experienced a merger event about 1 Gyr ago. On the assumption that these clusters are spreaded with similar density over the whole galaxy, the fraction of galaxy mass (5 x 10^{-5}) and rate of star formation (0.01 Msun/yr) involved, suggest the merger event as the possible cause for the star formation we see today.