Here is an additional image.

When all compartments are completely opened up, there are 29 slots/holes, approximately the size of pencil holders.

Here is an additional image.

Here is an additional image.

I'd suspect it to be church furniture based on the motto In hoc signo vinces. That message was given to Emperor Constantine ostensibly by god or something, and it accompanied the vision of a cross; "in this sign, conquer", and then the RC church became the official Roman religion. This is based on my foggy memories of Byzantine history. Or my Byzantine memories of foggy history.
My guess is you have a traveling communion kit.
Casey

Thank you, sombreuil_mongrel. That was so interesting. I really appreciate you taking the time to help me! :)

I'm wondering - traditionally a Pyx (host holder) would be a round lidded affair about the size of a pocket watch; usually in gold or silver. Although folk art examples do exist world wide made from available local materials.

Thinking also to the "Trial of the Pyx" in the UK where newly minted coins are presented to a jury to confirm they meet required standards. The coins are presented in a box called a pyx.

I'd question any religious significance in this case.

Sigma Chi fraternity crest ... writing box made in the orient for a Sigma Chi member.

Souvenir or gift? Dunno.

Here is a link that might be useful: Crest Info

Not a clue, but it is certainly an interesting piece. Please post when you get more information. Humidor made by a Sigma Chi who had lots of time and patience?