Unilateral Spatial Neglect, the most dramatic manifestation of contralesional space unawareness, is a highly heterogeneous syndrome. The presence of neglect is related to core spatially lateralized deficits, but its severity is also modulated by several domain-general factors (such as alertness or sustained attention) and by task demands. We previously showed that a computer-based dual-task paradigm exploiting both lateralized and non-lateralized factors (i.e., attentional load/multitasking) better captures this complex scenario and exacerbates deficits for the contralesional space after right hemisphere damage. Here we asked whether multitasking would reveal contralesional spatial disorders in chronic left-hemisphere damaged (LHD) stroke patients, a population in which impaired spatial processing is thought to be uncommon. Ten consecutive LHD patients with no signs of right-sided neglect at standard neuropsychological testing performed a computerized spatial monitoring task with and without concurrent secondary tasks (i.e., multitasking). Severe contralesional (right) space unawareness emerged in most patients under attentional load in both the visual and auditory modalities. Multitasking affected the detection of contralesional stimuli both when presented concurrently with an ipsilesional one (i.e., extinction for bilateral targets) and when presented in isolation (i.e., left neglect for right-sided targets). No spatial bias emerged in a control group of healthy elderly participants, who performed at ceiling, as well as in a second control group composed of patients with Mild Cognitive Impairment. We conclude that the pathological spatial bias in LHD patients cannot be attributed to a global reduction of cognitive resources but it is the consequence of unilateral brain damage. Clinical and theoretical implications of the load-dependent lack of awareness for contralesional hemispace following LHD are discussed.