We conducted a transmission electron microscope study of the exsolution microstructures of Ca-rich pyroxenes in type I chondrules from the Paris CM and Renazzo CR carbonaceous chondrites in order to provide better constraints on the cooling history of type I chondrules. Our study shows a high variability of composition in the augite grains at a submicrometer scale, reflecting nonequilibrium crystallization. The microstructure is closely related to the local composition and is thus variable inside augite grains. For compositions inside the pyroxene miscibility gap, with a wollastonite (Wo) content typically below 40mole%, the augite grains contain abundant exsolution lamellae on (001). For grain areas with composition close to Wo(40), a modulated texture on (100) and (001) is the dominant microstructure, while areas with compositions higher than Wo(40) do not show any exsolution microstructure development. To estimate the cooling rate, we used the spacing of the exsolution lamellae on (001), for which the growth is diffusion controlled and thus sensitive to the cooling rate. Despite the relatively homogeneous microstructures of augite grains with Wo<35mole%, our study of four chondrules suggests a range of cooling rates from 10 to 1000 degrees Ch(-1), within the temperature interval 1200-1350 degrees C. These cooling rates are comparable to those of type II chondrules, i.e., 1-1000 degrees Ch(-1). We conclude that the formation of type I and II chondrules in the proto-solar nebula was the result of a common mechanism.