The crystal structure and magnetic properties of CeNiH(3.7) were studied by means of powder x-ray diffraction, specific heat, and dc and ac magnetization techniques. It was established that hydrogenation stabilizes the 4f(1) state of Ce and turns CeNi-H into a dilute Kondo system with T(K) = 3.7 K. The Kondo screening in CeNiH(3.7) is suppressed by the applied magnetic field, although it still affects the properties of CeNiH(3.7) at 14 T, as indicated by the enhanced γ-coefficient of electronic specific heat, which remains more than twice as large as in the precursor compound CeNi. Its zero-field value is as high as 1890 mJ (mol K(2))(-1). Hydrogenation acts primarily as the negative pressure agent in CeNiH(3.7), while the role of H-metal bonding is secondary.