Chekrezi was born on 31 March 1892 in Ziçisht village, in the Upper Devoll region located near Korça, Ottoman Empire.

[2] After the Albanian Declaration of Independence until 1914 Chekrezi lived in Vlorë where he worked as a secretary in the Civil Court of the town, later as an interpreter for the International Control Commission assigned near Ismail Qemali's government and later Prince Wied.

[1] After being an active leader and participant of the Fier uprising of 1935,[3] he had to flee Albania to Italy together with his friends Musa Kranja and Xhevahir Arapi on an Italian fishing boat.

In 1946, he was the one to receive a delegation headed by Tuk Jakova in the New Yorker Hotel, and the second meeting with Mihal Prifti, where Costa suggested that the Albanian government should find the way to connect with the Western powers, especially the USA, and abolish the "friendly" relations with Yugoslavia of Tito, drawing parallels with King Zog-Nikola Pašić agreements.

[11] In the autumn of 1950, he hosted a meeting with Albanian representatives Behar Shtylla and Vilson Progri at the Governor Clinton Hotel.

In 1951, he published the political analysis "The third plan for partitioning Albania" in Washington D.C.[12] Constantin Chekrezi, was overshadowed for half a century by the communist regime; he died near Boston, on 10 January 1959, at the age of 66.

At his funeral, Fan Noli described him as a "statesman, who had struggled all his life for his nation, and a great Albanian guy who had to die poor".