Chahidi won for playing Maria in the all-male Twelfth Night at Shakespeare's Globe alongside Mark Rylance and Stephen Fry, which subsequently transferred to the West End and opens on Broadway next month.
The Awards were presented on Friday (13 September) at the Duke of York's Theatre on St Martin's Lane.
The Clarence Derwent Awards are given annually by Equity for the best individual male and female performances in a supporting role in a production in the West End.
This year's judges were critics Michael Billington and Kate Bassett, actor Peter Barnes, director Richard Digby Day, producer Thelma Holt and Equity president Malcolm Sinclair.
Sinclair said: "The judges were bowled over by the performances of Paul and Fenella. Paul has played the role of Maria a number of times in his career and his portrayal simply gets better and better. We thought that Fenella's role as the terrified friend of Hedda Gabler's schooldays was the key performance of that production."