The high radio-flux brightness temperature of the recently discovered class of sources known as Rotating RAdio Transients ( RRATs ) motivates detailed study in the X-ray band . The source RRAT J1911+00 has a ( large ) error region which includes the frequently observed low-mass X-ray binary transient Aql X-1 . We describe analyses of historical X-ray data , searching for X-ray phenomena ( sources , behaviors ) , finding no sources or behaviors which may unequivocally be associated with RRAT J1911+00 . We put forward a candidate X-ray counterpart to RRAT J1911+00 , discovered in a Chandra observation in Feb 2001 , which fades by a factor > 5 prior to April 2004 . Archival ROSAT observations detect the source as early as Oct 1992 , with a flux comparable to the Feb 2001 Chandra detection . The X-ray flux and optical ( F _ { X } / F _ { R } > 12 ) and near infra-red ( F _ { X } / F _ { J } > 35 ) limits , as well as the X-ray flux itself , are consistent with an AGN origin , unrelated to RRAT J1911+00 . Searches for msec X-ray bursts found no evidence for such a signal , and we place the first observational upper-limit on the X-ray to radio flux ratio of RRAT bursts : \mbox { $F _ { X } / F _ { 1.4 GHz } $ } < 6 \mbox { $ \times 10 ^ { -11 } $ } \mbox { $ erg$ } \ / % \mbox { $ \mbox { $ cm$ } ^ { -2 } $ } { s \mbox { $ { } ^ { -1 } $ } } \ / { mJy } ^ { -1 } . The upper-limit on the X-ray burst flux ( corresponding to < 2.2 \mbox { $ \times 10 ^ { 37 } $ } ( d / 3.3 \mbox { $ kpc$ } ) ^ { 2 } \mbox { $ erg$ } \ / ~ { % } { s \mbox { $ { } ^ { -1 } $ } } \ / , 2-10 keV ) requires a limit on the spectral energy density power-law slope of \alpha < -0.3 between the radio and X-ray bands . We place a limit on the time-average X-ray burst luminosity , associated with radio bursts , of \leq 3.4 \mbox { $ \times 10 ^ { 30 } $ } ( d / 3.3 \mbox { $ kpc$ } ) ^ { 2 } \mbox { $ erg% $ } \ / ~ { } { s \mbox { $ { } ^ { -1 } $ } } \ / . Future definitive association between CXOU J191121.3+003844 and RRAT J1911+00 could be made with a better radio localization of RRAT J1911+00 ; or discovery of msec X-ray bursts associated with the radio bursts . Adaptive optic infra-red observations of the crowded source field of CXOU J191121.3+003844 will be required to find a NIR counterpart , which may reveal its source class .