Focusing light deep inside living tissue has not been achieved despite its promise to play a central role in biomedical imaging, optical manipulation and therapy. To address this challenge, internal-guide-star-based wavefront engineering techniques--for example, time-reversed ultrasonically encoded (TRUE) optical focusing--were developed. The speeds of these techniques, however, were limited to no greater than 1 Hz, preventing them from in vivo applications. Here we improve the speed of optical focusing deep inside scattering media by two orders of magnitude, and focus diffuse light inside a dynamic scattering medium having a speckle correlation time as short as 5.6 ms, typical of living tissue. By imaging a target, we demonstrate the first focusing of diffuse light inside a dynamic scattering medium containing living tissue. Since the achieved focusing speed approaches the tissue decorrelation rate, this work is an important step towards in vivo deep tissue noninvasive optical imaging, optogenetics and photodynamic therapy.