Nanoacoustic strains are generated in Silicon by chirped femtosecond laser pulses using thin Titanium films as transducers. We investigate the effect that the generating laser pulse chirp has on the amplitude of the induced strains, manifested as Brillouin oscillations observed in degenerate femtosecond pump-probe transient reflectivity measurements. The strain amplitude is larger when negatively chirped pulses are used, which is attributed to the more efficient conversion of laser pulse light into acoustic strain in the Titanium transducer. Our present studies clearly show that the dependence of the Brillouin amplitude and the lattice strain is a non-monotonous function of the laser chirp parameter. An optimum negative laser pulse chirp is found for which the strain amplitude is maximized. A detailed thermomechanical model satisfactorily supports the experimental findings. In such a way, it is possible to suppress or enhance the induced nanoacoustic strain amplitude, thus all-optically controlling it by at least a factor of two.