When looking back on Irish Chess history the question arises who was Ireland's strongest chess player? You could take the amusing route and say Paul Morphy! Edward Winter in Chess Notes claims that the Morphy coat-of-arms is the same as that of Murphy's Stout. The site states: 'Thus the Morphy and Murphy family histories are shown to be inextricably linked'. I'm willing to say he was an Irishman!
Next flight of imagination - some books (incorrectly) claim that Steinitz won the Irish Championship in 1865! Therefore we may also be able to claim Steinitz.
OK! I'll leave the realms of fantasy now and settle for players born in Ireland. The choices available are Alexander MacDonnell (1798-1835), James Mason (1849-1905), and CHOD Alexander (1909-1974).
Alexander MacDonnell was of course famous for his series of matches against Labourdonnais. When looked at as a series of matches then MacDonnell could be considered as the unofficial world chess champion for a period after winning the second match. Also MacDonnell was leading in the last match when it was aborted.
My knowledge of James Mason is vague but Wikipedia states that research by Chessmetrics gives his chess strength at ELO 2715 and claim he was number one in the world between August 1877 and June 1878. (Wow, didn't know that!) Here's one for Carey! The opening 1.d4 d5 2.Bf4 is sometimes called the Mason Variation in his honour; he played it several times from the 1880s.
Finally CHOD Alexander. Though not in the same league as the above his claim to greatness must rest on his win against Botvinnik in the 1946 USSR-Great Britain radio match. Botvinnik was considered the best player in the world at this time.
This is just a brief look at this interesting question. Each of these players deserves to be examined on their own merits. In future articles I'm going to present a potted biography of each and present some of their best games.