What chambers are these?
Rashi: There were chambers in Chatzer ha'Penimi, to the north and south of Chatzer ha'Penimi, by its wall.
Radak: Also the cells are called Lishchos. They were around the Bayis.
Malbim: Perek 42 will explain that 20 Amos of Chatzer ha'Chitzonah next to Chatzer ha'Penimi received Kedushas ha'Azarah. One could eat Kodshei Kodoshim there. There were chambers in those 20 Amos along the entire wall of Chatzer ha'Penimi, which was 100 Amos long.
What was 20 Amos wide?
Rashi: The area between the walls of the chambers and the cells. This was not in Bayis Sheni, only in Bayis Shelishi.
Radak: There were 20 Amos between all the chambers.
Malbim: The chambers along the wall of Chatzer ha'Penimi, their width from north to south, with their walls, was 20 Amos. The verse teaches that 20 Amos was the width of the chambers around the wall that surrounds Chatzer ha'Penimi, 20 Amos from Chatzer ha'Penimi, which surrounds the Bayis. Why did the verse 'skip' to discuss chambers in Chatzer ha'Chitzonah? It is the introduction to the coming verse (refer to 41:11:2:2).