We present an analysis of two deep (75 ks) Chandra observations of the European Large Area 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 multi-wavelength 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 2 soft extended sources, which are found to be associated with galaxy clusters. An over-density of sources is found in N1 with 30% 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.