Scanning tunneling spectroscopy at very low temperature on homogeneously disordered superconducting Titanium Nitride thin films reveals strong spatial inhomogeneities of the superconducting gap ∆ in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature Tc towards zero, enhancement of spatial fluctuations in ∆, and growth of the ∆/Tc ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.PACS numbers: 74.50.+r, 74.78.Db, A pioneering idea that in the critical region of the superconductor-insulator transition (SIT) the disorderinduced inhomogeneous spatial structure of isolated superconducting droplets develops [1,2], grew into a new paradigm [3]. Extensive experimental research of critically disordered superconducting films revealed a wealth of unusual and striking phenomena, including nonmonotonic temperature and magnetic field dependence of the resistance [2,4,5,6], activated behavior of resistivity in the insulating state [1,5,6,7,8], nonmonotonic magnetic field dependence of the activation temperature, and the voltage threshold behavior [8,9,10]. These features find a theoretical explanation based on the concept of disorder-induced spatial inhomogeneity in the superconducting order parameter [10,11,12,13,14]. Numerical simulations confirmed that indeed in the high-disorder regime, the homogeneously disordered superconducting film breaks up into superconducting islands separated by an insulating sea [15,16]. At the same time the direct observation of superconducting islands near the SIT justifying the fundamental but yet hypothetical concept of the disorder-induced granularity on the firm experimental foundation was still lacking.In this Letter, we report on the combined low temperature Scanning Tunneling Spectroscopy (STS) and transport measurements performed on thin Titanium Nitride films on approach to the SIT. The local tunneling density of states (LDOS) measured at 50 mK reveals disorderinduced spatial fluctuations of the superconducting gap, ∆, with both, standard deviation σ to the average gap and the gap to the critical temperature ratios, σ/∆ and ∆/T c , respectively, increasing towards the transition.Our samples were thin TiN films synthesized by atomic layer chemical vapor deposition onto a Si/SiO 2 substrate. TiN1 was a 3.6 nm thick film deposited at 400• C while TiN2 and TiN3 were 5.0 nm thick films deposited at 350 • C. TiN3 was then slightly plasma etched in order to reduce its thickness. Electron transmission images revealed that the films comprise of the densely-packed crystallites with a typical size of 4 to 6 nm. The samples were patterned into the Hall bridges using conventional UV lithography and plasma etching. It is worth noticing that identically fabricated TiN films undergo the disorder-and magnetic field-driven SIT [4,8]. Transport measurements and STS were carried out during the same run in a STM attached to a dilution refrigerator. The STM Pt/Ir t...