Minaret of Bab al-Silsila
Commissioned in 1329, it is built in the traditional square style entirely out of stone and is located on the western side of the Temple Mount between the Ghawanima minaret (on the northwestern corner) and the Fakhariya minaret (on the southwestern corner). This minaret possibly replaced an earlier Umayyad minaret.
It was commissioned by the Mamluk's governor of Syria, Tankiz. Since the 16th century, this has traditionally had the most well-regarded muezzin of the minarets because it is the first to begin the call to prayer. After this minaret begins, then the rest of the minarets on the Temple Mount and Jerusalem follow suit.
Endnotes
http://www.enjoyjerusalem.com/explore/where-to-go/sabil-bab-al-silsila-chain-gate