Light-matter interaction is crucial in many application domains of nanophotonics, including biosensing, trapping at the nanoscale, nonlinear optics, and lasing. Many approaches, mainly based on photonic and plasmonic resonant structures, have been investigated to enhance and tailor the interaction, but those based on all-dielectric metasurfaces have several unique advantages: low loss, easy excitation and readout, possibility of engineering the optical field distribution with many degrees of freedom, and electric tuning. Here we show that properly designed all-dielectric metasurfaces can support silicon-slot quasi-bound states in the continuum modes resonating in the near-infrared, strongly confining light in air and, consequently, enhancing light-matter interaction. Some samples of the designed metasurface have been fabricated in a silicon-on-sapphire wafer by e-beam lithography and reactive ion etching. The optical characterization of the chip has confirmed the excitation of the quasi-bound state in the continuum resonant modes, with measured Q-factor values exceeding 700.