We investigate the spatial clustering of X-ray selected sources in the two deepest X-ray fields to date, namely the 2Ms Chandra Deep Field North (CDFN) and the 1Ms Chandra Deep Field South (CDFS). The projected correlation function w(r
p), measured on scales ∼0.2-10h
–1Mpc for a sample of 240 sources with spectroscopic redshift in the CDFN and 124 sources in the CDFS at a median redshift of z∼0.8 is used to constrain the amplitude and slope of the real space correlation function ξ(r)=(r/r
0)
–γ. The clustering signal is detected at high confidence (>7σ) in both fields. The amplitude of the correlation is found to be significantly different in the two fields, the correlation length r
0 being 8.6±1.2h
–1Mpc in the CDFS and 4.2±0.4h
–1Mpc in the CDFN, while the correlation slope γ is found to be flat in both fields: γ=1.33±0.11 in the CDFS and γ=1.42±0.07 in the CDFN (a flat Universe with Ω
m=0.3 and Ω
Λ=0.7 is assumed; 1σ Poisson error estimates are considered). The correlation function also has been measured separately for sources classified as AGN or galaxies. In both fields AGN have a median redshift of z∼0.9 and a median 0.5-10keV luminosity of L
x∼10
43 erg/s, i.e. they are generally in the Seyfert luminosity regime. As in the case of the total samples, we found a significant difference in the AGN clustering amplitude between the two fields, the best fit correlation parameters being r
0=10.3±1.7h
–1Mpc, γ=1.33±0.14 in the CDFS, and r
0=5.5±0.6h
–1Mpc, γ=1.50±0.12 in the CDFN. In the CDFN, where the statistics are sufficiently high, we were also able to measure the clustering of X-ray selected galaxies, finding r
0=4.0±0.7h
–1Mpc and γ=1.36±0.15 . Within each field no statistically significant difference is found between soft and hard X-ray selected sources or between type 1 and type 2 AGN. After having discussed and ruled out the possibility that the observed variance in the clustering amplitude is due to observational biases, we verified that the extra correlation signal in the CDFS is primarily due to the two prominent redshift spikes at z∼0.7 reported by Gilli et al. (
2003ApJ...592..721G). The high (5-10h
–1Mpc) correlation length measured for the X-ray selected AGN at z∼1 in the two Chandra Ms fields is comparable to that of early type galaxies at the same redshift. This is consistent with the idea that, at z∼1, AGN with Seyfert-like luminosities might be generally hosted by massive galaxies.