Into the Wardrobe

I found a copy of "The Silver Chair" at a thrift store today, and I am not sure if it is a 1st edition or not. It is copyright 1953 by Macmillan in the United States. It is hardcover, but it doesn't have a sleeve on it. I looked images up online and they look exactly like my book, except a different color. Mine is brown/orange, and the pictures I saw were blue/green.
No where in the book does it state that it is a first edition, and I read that some of them do.
Does anyone have any experience with identifying these?

Welcome, JenniWren!

According to Edwin Brown's guide to Lewis first editions, the US first is a very dark blue cloth, not brown/orange. On the back of the title page is printed in bold First Printing.