This paper presents light scattering measurements of the aggregation rate for an aerosol of fractal aggregates in a rarefied gas. A premixed ethylene/oxygen flame was used to create a hot, fractal aggregate aerosol of carbonaceous soot. Static light scattering involving absolute scattering, extinction, and optical structure factor measurements was used to measure the soot cluster morphological parameters, cluster radius of gyration, fractal dimension, monomers per aggregate and monomer size, all as a function of height above burner. Laser Doppler velocimetry was used to convert height to time. Above a height of 7 mm, it was established that aggregation was the dominant growth mechanism. The aggregation cluster growth kinetics are compared to the Smoluchowski equation prediction using an aggregation kernel that accounts for the fractal nature of the aggregates. The kinetics of this system ranged from the free molecular to the Epstein regime. Comparison of experiment to theory shows the theory to be from 15 to 100% too low which may be compared to an experimental uncertainty of a factor of two due largely to soot particle refractive index uncertainty. The discrepancy could be due to attractive dispersive forces between aerosol particles. These discrepancies are small, however, compared to the range of the aggregation kernel. Hence this work establishes the validity of the theoretical form of the kernel for fractal aggregates in rarefied gases.