This study is being conducted to determine the best confirmed response rate, safety, and tolerability of GSK1363089 treatment in adult subjects with squamous cell carcinoma of the head and neck (SCCHN). GSK1363089 is a new chemical entity that inhibits multiple receptor tyrosine kinases (RTKs) with growth-promoting and angiogenic properties. The primary targets of GSK1363089 are the HGF and vascular endothelial growth factor (VEGF) RTK families (eg, MET, VEGFR2/kinase insert domain receptor [KDR]). Since MET overexpression has been associated with poorer prognosis and MET tyrosine kinase mutations have been reported in SCCHN, inhibition of MET receptor and VEGFR2/KDR activation by agents such as GSK1363089 may be of therapeutic benefit in this patient population.