Coronal heating may be a result of frequent microscopic energy releases, which Parker has termed nanoflares. Since solar radio type I bursts, which are frequently observed at meter wavelengths, involve extremely small amount of energy, we have determined the frequency distribution of the peak flux density of these bursts. The study has been performed on 11 noise storm events observed by the Nancay Radioheliograph at 164, 237, and 327 MHz. At each frequency, and for the 11 noise storms, the peak flux density distribution of type I bursts can be well represented by a power law. The index α of the distribution, ~3, is nearly independent of the observing frequency and does not vary much from one noise storm to the other, i.e., from one active region to the other. This index is significantly steeper than that measured for various other flare phenomena (<2). There are noise storm theories and various spectral and imaging radio observations that suggest that type I bursts may be a nonthermal signature of energy release fragments. If this is the case, such a steep power-law distribution is consistent with the prediction of avalanche models developed for small energy release events reminiscent of nanoflares, as well as the idea that small energy release events may contribute to the heating of an active coronal region.