I revised table B by adding a column and an additional vaue of A_ID:

CREATE Table #B(B_ID INT,A_ID INT,City VARCHAR(5),State VARCHAR(2),Zip VARCHAR(10),Entered DATETIME)

INSERT INTO #B

SELECT 1,1,'xxx','TN','37013',GETDATE() UNION ALL

SELECT 2,1,'yyy','TX','37012',GETDATE() - 40 UNION ALL

SELECT 2,2,'aaa','UT','44030', GETDATE() - 5

Then try this code:

;with numbered as(SELECT rowno=row_number() over

(partition by A_id order by entered ASC),A_Id,B_Id,city,state,zip,entered from #B) --

SELECT A.F_name,A.M_Name,A.L_Name1, N.A_id,N.City, N.State, N.Zip,N.Entered

FROM numbered AS N

INNER JOIN #A AS A ON A.A_id = N.A_id WHERE rowno = 1

Results:

F_nameM_NameL_Name1A_idCityStateZipEntered

ABC1yyyTX370122010-06-21 11:42:13.187

XYZ2aaaUT440302010-07-26 11:42:13.187

If this is not what you require please repost listing what I missed, or how I misundersood your requirements.