Supernovae play a key role in the dynamics, structure, and chemical evolution of galaxies. The massive stars that end their lives as supernovae live for short times. Many are still associated with dusty star formation regions when they explode, making them difficult to observe at visible wavelengths. In active star forming regions (galactic nuclei and starburst regions), dust extintion is especially severe. Thus, determining the supernova rate in the active star forming regions of galaxies, where the supernova rate can be one or two orders of magnitude higher than the average, has proven to be difficult. From observations of SN1987A, we know that the [NiII] 6.63 micron emission line was the strongest line in the infrared spectrum for a period of a year and a half after the explosion. Since dust extintion is much less at 6.63 pm than at visible wavelengths (A(sub 6.63)/A(sub V) = 0.025), the NiII line can be used as a sensitive probe for the detection of recent supernovae. We have observed a sample of starburst galaxies at 6.63 micron using ISOCAM to search for the NiII emission line characteristic of recent supernovae. We did not detect any NiII line emission brighter than a 5sigma limit of 5 mJy. We can set upper limits to the supernova rate in our sample, scaled to the rate in M82, of less than 0.3 per year at the 90% confidence level using Bayesian methods. Assuming that a supernova would have a NiII with the same luminosity as observed in SN1987A, we find less than 0.09 and 0.15 per year at the 50% and 67% confidence levels. These rates are somewhat less if a more normal type II supernovae has a NiII line luminosity greater than the line in SN1987A.