We identify a pair of near-degenerate states of opposite parity in atomic Xe, the $5p^5 10s ,, ^2[3/2]_2^o$ at $rm{E}=94759.927$ cm$^{-1}$ and $5p^5 6f ,, ^2[5/2]_2$ at $rm{E}= 94759.935$ cm$^{-1}$, for which parity- and time-odd effects are expected
to be enhanced by the small energy separation. We present theoretical calculations which indicate narrow widths for both states and we report a calculated value for the weak matrix element, arising from configuration mixing, of $|W|=2.1$ Hz for $^{132}$Xe. In addition, we measured the Stark effect of the $5p^5,6f$ $^2[5/2]_{2}$ and $5p^5 ,6f ^2[3/2]_2$ ($rm{E} =94737.121,rm{cm}^{-1}$) states. The Stark-shift of the $6f$ states is observed to be negative, revealing the presence of nearby $6g$ states at higher energies, which have not been observed before. The Stark-shift measurements imply an upper limit on the weak matrix element of $|W|!<!5$ Hz for the near-degenerate states ($10s ,, ^2[3/2]_2^o$ and $6f ,, ^2[5/2]_2$), which is in agreement with the presented calculations.
