SONYC -- Substellar Objects in Nearby Young Clusters -- is a survey program to investigate the frequency and properties of substellar objects with masses down to a few times that of Jupiter in nearby star-forming regions. Here we present the first results from SONYC observations of NGC1333, a ~1Myr old cluster in the Perseus star-forming complex. We have carried out extremely deep optical and near-infrared imaging in four bands (i, z, J, K) using Suprime-Cam and MOIRCS instruments at the Subaru telescope. The survey covers 0.25sqdeg and reaches completeness limits of 24.7mag in the i-band and 20.8mag in the J-band. We select 196 candidates with colors as expected for young, very low-mass objects. Follow-up multi-object spectroscopy with MOIRCS is presented for 53 objects. We confirm 19 objects as likely brown dwarfs in NGC1333, seven of them previously known. For 11 of them, we confirm the presence of disks based on Spitzer/IRAC photometry. The effective temperatures for the brown dwarf sample range from 2500K to 3000K, which translates to masses of ~0.015 to 0.1Ms. For comparison, the completeness limit of our survey translates to mass limits of 0.004Ms for Av<~5mag or 0.008Ms for Av<~ 10mag. Compared with other star-forming regions, NGC1333 shows an overabundance of brown dwarfs relative to low-mass stars, by a factor of 2-5. On the other hand, NGC1333 has a deficit of planetary-mass objects: Based on the surveys in SOrionis, the ONC and Cha I, the expected number of planetary-mass objects in NGC1333 is 8-10, but we find none. It is plausible that our survey has detected the minimum mass limit for star formation in this particular cluster, at around 0.012-0.02Ms. If confirmed, our findings point to significant regional/environmental differences in the number of brown dwarfs and the minimum mass of the IMF. (abridged)
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