|Covid-19|January 27 – Pope Clement VI issues his Bull Unigenitus, defining the doctrine of "The Treasury of Merits" or "The Treasury of the Church" as the basis for the issuance of indulgences by the Catholic Church.
April 23 – Beginning of the St. George's Night Uprising in Estonia.
May 4 – The St. George's Night Uprising: The "four Estonian kings" are murdered at the negotiations with the Livonian Order.
August 15 – Magnus IV of Sweden abdicates from the throne of Norway in favor of his son Haakon VI of Norway. However Haakon is still a minor, allowing Magnus to remain de facto ruler.
August 31 – A naval league is formed between the Pope, the Republic of Venice, the Knights Hospitaller and the Kingdom of Cyprus, to prepare the Smyrniote crusades.
November 25 – A tsunami, caused by an earthquake, devastates the Maritime Republic of Amalfi, among other places.
Emperor Chōkei of Japan (d. 1394)
Constance of Aragon, queen consort of Sicily (d. 1363)
Thomas Percy, 1st Earl of Worcester, English rebel (d. 1403)
Tommaso Mocenigo, doge of Venice (d. 1423)
Paolo Alboino della Scala, lord of Verona (d. 1375)
Alexander Stewart, 1st Earl of Buchan (d. 1394)
probable – Geoffrey Chaucer, English poet (approximate date) (d. 1400)
January 20 – Robert of Naples (b. 1277)
May 29 – Francesco I Manfredi, lord of Faenza
June 22 – Aimone, Count of Savoy (b. 1291)
June 23 – Giacomo Gaetani Stefaneschi, Italian cardinal (b. c. 1270)
September 16 – Philip III of Navarre (b. 1306)
December 15 – Hasan Kucek, Chobanid prince (b. c. 1319)
Sir Ulick Burke, Irish nobleman
Veera Ballala III, ruler of the Hoysala Empire (b. 1291)
Year 1343 (MCCCXLIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar.