Chalmers, who also won the Australian Open earlier in the month, jumped up 40 places this week.
Luke Donald celebrated six months atop the world rankings, followed by Rory McIlroy, Lee Westwood and Martin Kaymer. Dustin Johnson and Steve Stricker switched places with Johnson now fifth and the highest-ranked American and Stricker down to No. 6.
Matt Kuchar, who teamed with Gary Woodland to win the World Cup, dropped one to 11th. Phil Mickelson, Charl Schwartzel, Graeme McDowell, K.J. Choi, Justin Rose, Sergio Garcia, Bubba Watson, Hunter Mahan and David Toms rounded out the top 20.