Context : Aims : I study the spectral , temporal and spatial characteristics of the quiescent X-ray emission ( not in outburst ) of the recurrent nova T Pyx . Methods : I perform the spectral analysis of the X-ray data obtained using the Chandra Observatory , Advanced CCD Imaging Spectrometer ( ACIS-S3 ) detector . I calculate the light curve of the data and perform power spectral analysis using Fourier transform . Finally , I do high-resolution imaging analysis of the data at the sub-pixel level . Results : I present a total of 98.8 ksec ( \sim 3 \times 30 ksec ) observation of T Pyx obtained with the ACIS-S3 detector on-board the Chandra Observatory obtained during the quiescent phase , about 2-3 months before its outburst in April 2011 . The total Chandra spectrum of the source T Pyx gives a maximum temperature kT _ { max } > 37.0 keV ( 2 \sigma lower limit ) with ( 0.9-1.5 ) \times 10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } and ( 1.3-2.2 ) \times 10 ^ { 32 } erg s ^ { -1 } ( at 3.5 kpc ) in the 0.1-50 keV range using a multi-temperature plasma emission model ( i.e. , CEVMKL in XSPEC ) . I find a ratio of ( L _ { x } /L _ { disk } ) \simeq ( 2-7 ) \times 10 ^ { -4 } ( assuming L _ { disk } \sim 3 \times 10 ^ { 35 } erg s ^ { -1 } ) indicating considerable inefficiency of emission in the boundary layer . There is no soft X-ray blackbody emission with a 2 \sigma upper limit on the blackbody temperature and luminosity as kT _ { BB } < 25 eV and L _ { soft } < 2.0 \times 10 ^ { 33 } erg s ^ { -1 } in the 0.1-10.0 keV band . All fits yield only interstellar N { { } _ { H } } during quiescence . I suggest that T Pyx has an optically thin boundary layer ( BL ) merged with an ADAF-like flow ( Advection-Dominated Flow ) and/or X-ray corona in the inner disk indicating ongoing quasi-spherical accretion at ( very ) high rates during quiescent phases . Such a BL structure may be excessively heating the WD , influencing the thermonuclear runaway leading to the recurrent nova events . The orbital period of the system is detected in the power spectrum of the Chandra light curves . The central source ( i.e. , the binary system ) emission and its spectrum is deconvolved from any extended emission with a detailed procedure at the sub-pixel level revealing an extended emission with S/N \sim 6-10 . The derived shape looks like an elliptical nebula with a semi-major axis \sim 1.0 arcsec and a semi-minor axis \sim 0.5 arcsec , also indicating an elongation towards south . The calculated approximate count rate of the extended emission is 0.0013-0.0025 c s ^ { -1 } . The luminosity ( within errors ) of the nebula is \sim ( 0.6-30.0 ) \times 10 ^ { 31 } erg s ^ { -1 } ( at 3.5 kpc ) mostly correct towards the lower end of the range . The nebulosity seems consistent with an interaction of the outflow/ejecta from the 1966 outburst . Conclusions :