Hello, and thanks for clarifying (in dms) which section of the Epic this comes from - it's Tablet III, lines 148-154. The word in question is the Akkadian bīt, which means "house" or "building", and is the root of many more specific terms for different buildings. It could also be used for "temple" or various other kinds of structures. It's the equivalent of the Sumerian e, which has the same set of meanings, and both are written 𒂍 in cuneiform.
George was, like many modern translators, presumably trying to make the text as recognizable as possible to his (assumed) reader, so used "chapel" as a creative liberty. Helle (2021) here uses "temple" with the same surrounding phrasing: "Enkidu in the temple of ... / and Gilgamesh in the temple of ..."
The term used for the temple of Ninsun earlier in tablet III is egalmah, a Sumerian term that literally means "great big building", but is used for a major temple. It starts with the same e sign, 𒂍. Given that we don't know what comes after bīt in the lines here, it's possible it was egalmah, but without a more complete version of this section we can't know for sure. The term bīt is also used in this tablet as part of the phrase for "bath-house" (bīt narmaku III.37), illustrating its more generic "building/house" meaning.
If I were to translate this, I'd probably use "building", just because the lack of context makes any more specific term seem too confident in meaning (this section is extremely fragmentary). As to what this section refers to, it could basically be anything - though if any Akkadianists have thoughts, please reblog with them! And thank you again for your question.