Why was Becket appointed chancellor?
When King Henry II came to power in 1154, the English church wanted an Englishman to take up his chancery, rather than a Norman or another foreigner. Becket, backed by Theobald, was their choice. Becket's life drastically changed, as he was on the largest salary of all household officials. He was at the centre of the government, acting as a diplomat, ambassador and advisor.

Why was Becket chosen?
1) Becket would be well placed to serve YH, who Henry was planning on crowing in his own reign.
2) Henry believed that Thomas, as chancellor, would be his man in the growing rights and powers of the church

In Germany Frederick Barbarossa had appointed his chancellor as archbishop in 1159. He had served his emperor well, continuing to seveve his temporal and spiritual masters without conflict or strain, therefore Henry expected Becket do to the same

The higher clergy, such as Archbishop Roger of York, and the Bishop of London, strongly objected to this 'outside' appointment for archbishop

Henry saw improvement in the law as being a major factor in bringing greater stability to England, in the wake of the chaos of Stephen