The internal decor of your house displays not only your public persona but also the atmosphere in which you choose to dwell. The care you exert in choosing religiously appropriate objects in your home express your commitment to Judaism above, or at least in conjunction with, esthetics.
A chess set often serves as both decoration and entertainment. However, the game’s most important piece poses a dilemma to Jewish players. The king is generally adorned with a cross. A cross represents Christianity, reminding us of the religion’s foundational claim and also the centuries of Christian persecution Jews have suffered. The latter is an emotional claim but the former is legal. Jewish law prohibits the ownership of a foreign religious object. Must a Jew, therefore, break the cross on his king?
Jewish legal authorities have long debated the status of the Christian concept of trinity — is it monotheism or polytheism? While this may seem like it should be the crux of the issue (pardon the pun), it actually has no bearing on the outcome. Even those who accept that Christianity is a fine religion for gentiles, who are bound by the Noahide covenant to avoid idolatry and polytheism, consider the religion to be a forbidden foreign religion for Jews.
Thus, R. David Tzvi Hoffmann (Melamed Le-Ho’il 1:16) prohibits Jews from using an organ in synagogue because it is a Christian practice. Even though he holds that Christianity is permissible for gentiles, he considers it entirely forbidden for Jews. More to the point, both Rema (Shulchan Arukh, Orach Chaim 156:1) and Shakh (Yoreh De’ah 153:7) rule that Christianity is acceptable for gentiles (see Pischei Teshuvah, Yoreh De’ah 147:5) but forbid crosses as impermissible to Jews (Yoreh De’ah 141:3 and Shakh, ad loc. 6). The Avnei Neizer (122) struggles to find a reason to allow a Jew to let a hostile Russian township build a large cross on his property, successfully finding a leniency so the Jew need not forfeit his life to avoid the severity of this prohibition. Even the most accepting authorities see Christianity as a religion Jews must avoid at all cost.
If crosses represent a foreign religion to which Jews may not submit, may a Jew ever own one? This question arose for Jewish merchants who sometimes traded in religious jewelery. Can they sell decorative crosses? Rema (Shulchan Arukh, Yoreh De’ah 141:3) records a leniency. While you may not obtain even indirect benefit from an item used for a foreign religion, you may sell an item that serves only a decorative purpose. Since no one has worshiped with the object, it is not forbidden.
However, the Chokhmas Adam (85:2) points out, this leniency only allows you to derive benefit from the item. You still may not own it because people might think that it is your religious object. The only exception is an item that is used disrespectfully, in a way that no one would treat a religious object. Similarly, Nachal Eshkol (Hilkhos Avodah Zarah n. 50, quoted in She’arim Metzuyanim Ba-Halakhah 167:2 kuntres acharon) permits owning an oven with a cross on it. Since no one uses it for religious purposes, it is considered “disrespectful” and allowed.
Based on this, we might suggest (this is just a suggestion) that since a chess piece is also never used for religious purposes, it is considered a “disrespectful” item that a Jew may own. No one will think that it is your religious object because it simply is not one. It is a game piece.
Even if this is correct, the Jewish aversion to crosses is a long-standing tradition. R. Chaim Soloveitchik would even rearrange silverware that happened to be placed like a cross (Nefesh Ha-Rav, p. 230). There is certainly room for Jews to refuse to decorate their houses with a chess piece containing a cross and instead break it to remove reminders of a foreign religion and a very violent history.