We have detected significant X-ray emission from the direction of the young radio pulsar PSR J1105 - 6107 using the ASCA Observatory . The 11 \sigma detection includes 460 background-subtracted source counts derived using data from all four ASCA detectors . The emission shows no evidence of pulsations ; the pulsed fraction is less than 31 % , at the 90 % confidence level . The X-ray emission can be characterized by a power-law spectrum with photon index \alpha = 1.8 \pm 0.4 , for a neutral hydrogen column density N _ { H } = 7 \times 10 ^ { 21 } cm ^ { -2 } . The unabsorbed 2 - 10 keV flux assuming the power-law model is ( 6.4 \pm 0.8 ) \times 10 ^ { -13 } ergs cm ^ { -2 } s ^ { -1 } . The implied efficiency for conversion of spin-down luminosity to ASCA -band emission is ( 1.6 \pm 0.2 ) \times 10 ^ { -3 } , assuming a distance of 7 kpc to the source . Within the limited statistics , the source is consistent with being unresolved . We argue that the X-rays are best explained as originating from a pulsar-powered synchrotron nebula .