November 17 is "Shogi Day"
Though I don't know if there is "Chess Day", I would like to write something about "Shogi Day" in Japan. It was established by Japan Shogi Association. Here is the origin of the day.
Shogi Day was established in 1975 with the aims of promoting the diffusion of Shogi as a traditional culture and stimulating exchange with Shogi fans. It has its origins in Castle Shogi, one of the annual events held by the Shogunate in the Edo period, in which the three iemoto Shogi Families played a match before the Shogun in Edo Castle. In 1716, the eighth Shogun Tokugawa Yoshimune designed November 17 as the date for the Castle Shogi tournament. Accordingly, various events have been held around this date every year since 1975. - extracted from the pamphlet of The International Shogi Festival 2008 in Tendo