N.M. Stat. § 4-8-1
That the counties of Chaves and Eddy are hereby created out of all that portion of Lincoln county, lying eastward of a line drawn through said county as follows, to wit: commencing at the northern boundary line of the county of Lincoln on the line between ranges nineteen and twenty east; thence south on said line to the base line; thence south along the range line between ranges nineteen and twenty east to the first standard parallel south; thence east to the point where the range line between ranges twenty and twenty-one east, south of said first standard parallel intersects said parallel; thence south on the line between said ranges twenty and twenty-one to the second standard parallel south; thence south to the southeast corner of township eleven south of range twenty east; thence west to the line between ranges twenty and twenty-one south of the second standard parallel south; thence south to the third standard parallel south along the range line between ranges twenty and twenty-one to intersect the third standard parallel south; thence east along said parallel to where the line from the south side of same between ranges twenty-one and twenty-two intersects said parallel; thence along said range line between ranges twenty-one and twenty-two to the fourth standard parallel south; thence west along said parallel to the point where the line between ranges twenty-one and twenty-two south of said parallel intersects said parallel, and thence south on said line to the north boundary of the state of Texas.
NMS § 4-8-1