We present an analysis of two deep (75 ks) Chandra observations of the European Large Area Infrared Space Observatory (ISO) Survey (ELAIS) fields N1 and N2 as the first results from the ELAIS deep X-ray survey. This survey is being conducted in well-studied regions with extensive multiwavelength coverage. Here we present the Chandra source catalogues along with an analysis of source counts, hardness ratios and optical classifications. A total of 233 X-ray point sources are detected in addition to two soft extended sources, which are found to be associated with galaxy clusters. An overdensity of sources is found in N1 with 30 per cent more sources than N2, which we attribute to large-scale structure. A similar variance is seen between other deep Chandra surveys. The source count statistics reveal an increasing fraction of hard sources at fainter fluxes. The number of galaxy-like counterparts also increases dramatically towards fainter fluxes, consistent with the emergence of a large population of obscured sources.