Place for a Lady chapel (4)

I believe the answer is:

apse

(Other definitions for apse that I've seen before include "Offshoot from the choir, nave or aisle in a church" , "Strange peas in the church recess" , "Recess at east end of church" , "Niche in church" , "Large recess in church" .)

I've seen this clue in The New York Times.

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