In the introductory statement to Hilchos Chanuka in Mor U' Ketziah , R' Yakov Emden writes:
meaning that many had the custom to spend the nights of Chanuka playing chess, dominoes (?), cards (See R' Brodt's post on cardplaying here),
[The rest of the statement is hard to follow (I am surprised that Prof. Schacter didn't add some explanatory note) although the same expression appears in Yaavetz's commentary to Avot:
המרימים קולם בחלוק ובלוק בערמה • באסקינדרי איטללו בנרדשיד וגורייתא . הללו מכלי עילם . עושין מעשי זמרי ומבקשין שכר כפנחס • חוטאים ומחטיאים וממלאים הארץ זמה ]
The same custom of playing chess on Chanuka can also be found in the book of Minhagim of Worms that forbids gambling except in the case of chess (see v. 1 pg. 343). R' Yaakov Emden in the additions to his siddur forbids his descendants to play any game of skill except for chess in order to sharpen the mind a bit (but for no longer then an hour).
The Maharal also knows of the benefits of chess in sharpening the mind anin one of his famous polemics against pilpul (Tiferet Yisroel pg. 168) he writes:
People believe that one can develop into a Torah scholar only through the mental gymnastics of pilpul, which posits theories of halakha and then analyzes these empty contrived hypotheses. They create new explanations of Torah that are unfounded, claiming that this method is necessary to sharpen the mind. How can they think like that? A person should tear his heart out over this practice of turning truth into falsehood in order to sharpen the mind! Such a thing should not be found in Israel - to sharpen the mind with falsehood or to even spend time on falsehood - for the Torah is a Torah of truth. Indeed, as a result, they become more foolish, rather than wiser. It would be better to learn carpentry or another trade, or to sharpen the mind by playing chess. At least they would not engage in falsehood, which then spills over from theory and into practice...
Chavos Yair mentions chess in his Mekor Chaim (siman 338 - cited in the excellent notes to the Minhag book):
but I have not yet had a chance to follow his references. I think this means - שיק צום פעלד - send (the army) to the field (of battle) but see aforementioned notes.
One of the more interesting aspects of Chabad theology is a lengthy dissertation on Chess as an allegory for Avodas HaShem that can be found in Yemei Bereishis pg. 337 ff. which also has a pictures of the Lubavitcher Rebbe Z"l and his Father in law, deeply engrossed in a game of chess on the night of Nitel.