Born in Glasgow, he signed for David Calderhead's Chelsea as a junior from local club Bridgeton Waverley and made his debut for the club in 1926 against Bradford City. He soon established himself as Chelsea's first choice full-back, a position he would hold for most of his time at Stamford Bridge and was one of the less glamorous, though more reliable, members of a star-studded Chelsea squad which included his Scottish teammates, Hughie Gallacher, Alex Jackson, Willie Ferguson and Andy Wilson. He made 318 appearances for Chelsea, scoring 19 goals, mainly from penalties.
Law won two caps for Scotland, both against England. He made his debut during Scotland's famous "Wembley Wizards" 5-1 win over England at Wembley in 1928. His final cap came two years later, though this time the Scots lost 2-5.
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