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18 pags, 11 figs, 5 tabs ; Here, we illustrate what happens inside the catalytic cleft of an enzyme when substrate or ligand binds on single-millisecond timescales. The initial phase of the enzymatic cycle is observed with near-atomic resolution using the most advanced X-ray source currently available: the European XFEL (EuXFEL). The high repetition rate of the EuXFEL combined with our mix-and-inject technology enables the initial phase of ceftriaxone binding to the Mycobacterium tuberculosis β-lactamase to be followed using time-resolved crystallography in real time. It is shown how a diffusion coefficient in enzyme crystals can be derived directly from the X-ray data, enabling the determination of ligand and enzyme-ligand concentrations at any position in the crystal volume as a function of time. In addition, the structure of the irreversible inhibitor sulbactam bound to the enzyme at a 66 ms time delay after mixing is described. This demonstrates that the EuXFEL can be used as an important tool for biomedically relevant research. ; This work was supported by the National Science Foundation Science and Technology Center 'BioXFEL' through award STC-1231306, and in part by the US Department of Energy, Office of Science, Basic Energy Sciences under contract DESC0002164 (AO, algorithm design and development) and by the National Science Foundation under contract Nos. 1551489 (AO, underlying analytical models) and DBI-2029533 (AO, functional conformations). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1450681 to JLO. The work was also supported by funds from the National Institutes of Health grant R01 GM117342-0404. Funding and support are also acknowledged from the National Institutes of Health grant R01 GM095583, from the Biodesign Center for Applied Structural Discovery at ASU, from National Science Foundation award No. 1565180 and the US Department of Energy through Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. KAZ was supported by the Cornell Molecular Biophysics Training Program (NIH T32-GM008267). This work was also supported by the Cluster of Excellence 'CUI: Advanced Imaging of Matter' of the Deutsche Forschungsgemeinschaft (DFG), EXC 2056, project ID 390715994. CFEL is supported by the Gottfried Wilhelm Leibniz Program of the DFG, the 'X-probe' project funded by the European Union 2020 Research and Innovation Program under Marie Sklodowska-Curie grant agreement 637295, the European Research Council, 'Frontiers in Attosecond X-ray Science: Imaging and Spectroscopy (AXSIS)', ERC-2013-SyG 609920, and the Human Frontiers Science Program grant RGP0010 2017. This work is also supported by the AXSIS project funded by the European Research Council under the European Union Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement No. 609920. ; Peer reviewed