We present the results of a measurement of the near-infrared extragalactic background light (EBL). The surface brightness towards the opaque intermediate-latitude globule DC303.8-14.2 was obtained using ESO VLT/FORS spectrophotometry. Long-slit spectra covering the opaque core and the almost unobscured area north of the cloud were measured using the nodding-along-the-slit measuring technique, thus providing a differential spectrum opaque core – transparent area. It is free of most of the foreground components, also excluding most of the airglow time variations. The scattered integrated starlight (ISL) from the dark core itself is the only remaining major foreground component when extracting the EBL from the differential spectrum. The scattered starlight spectrum in the wavelength domain 8450–8700 Å is dominated by the strong Ca II triplet Fraunhofer lines at λ 8498, 8542, 8664 Å, whereas the integrated light of galaxies and other contributors to the EBL intensity produce a smooth spectrum without these lines. We used the GAIA RVS spectral database to construct a template for the scattered ISL spectrum; another template was obtained by using the globule’s semi-transparent bright rim. The resulting EBL intensity as derived from the λ 8542 Å line is I_EBL = 1.62 ± 0.76(σ_stat) 10⁻⁹ erg cm⁻² s⁻¹ Å⁻¹ sterad⁻¹ or 13.8 ± 6.5(σ_stat) nW m⁻² sr⁻¹; this represents a tentative detection at 2.1σ level; the scaling uncertainty is ±10%.