Dallas was born in
Kingston, Jamaica, to Robert Charles Dallas, Sr. and Sarah Elizabeth (Cormack) Hewitt. His brother was
Robert Charles Dallas, who wrote a history of the
Jamaican Maroons. Dallas bought the Boar Castle estate on the Cane River, Jamaica in 1758, changing its name to Dallas Castle. This property included 900 acres and 91 slaves. Dallas left the island in 1764, having mortgaged the estate and put it in a trust. When Alexander was five, his family moved to
Edinburgh and then to London. There he studied under
James Elphinston, a Scottish educator and linguist. He planned to study law, but was unable to afford it. In 1780, Alexander married Arabella Maria Smith (1761–1837) of Pennsylvania. Arabella came from a family lineage with prominent connections to the British military as the daughter of Major George Smith of the British Army and Arabella Barlow, and a great-granddaughter of Sir Nicholas Trevanion, by way of Reverend William Barlow and Arabella Trevanion. In 1781, they moved to Jamaica. There, Alexander was
admitted to the bar through his father's connections. However, Maria's health suffered in Jamaica, and they subsequently moved to
Philadelphia in 1783, where he was admitted to the Pennsylvania bar in 1785. To supplement his budding law practice, he also took side jobs editing the
Pennsylvania Herald from 1787 to 1788 and the
Columbian Magazine from 1787 to 1789. ==U.S. Supreme Court Reporter==