Luckily the two teams don't play very often.
The Chiefs are 4-5 all-time against the Saints, their Week 3 opponent. KC lost the last two meetings against the Saints -- 30-20 in 2008 and 27-20 in 2004.
These are two totally different teams, obviously, since the last time they met. Tyler Thigpen was throwing passes for the Chiefs in 2008. Dwayne Bowe was still catching touchdowns though. Two of them in fact.
Chiefs vs. Saints history (wins in bold...via Chiefs game release)
11/16/08 L, 30-20 in Kansas City
11/14/04 L, 27-20 in New Orleans
12/21/97 W, 25-13 in Kansas City
9/4/94 W, 30-17 in New Orleans
9/8/91 L, 17-10 in Kansas City
9/8/85 W, 47-27 in New Orleans
11/21/82 L, 27-17 in New Orleans
9/26/76 L, 27-17 in Kansas City
9/25/72 W, 20-17 in New Orleans