The easiest way to win 2000 chips in one hand is to reach the High Stakes poker table in the hotel of Blackwater. There, you start with 2500 chips. Since everyone always fold on the first hand, you win your bet (2500 chips) and get the achievement :)
*In order to reach the High Stakes poker table, you must wear the Gentleman`s Attire outfit which can be earned by subscribing to the Rockstar Social Club:http://socialclub.rockstargames.com/games/rdr
Edit : If going All-in do not give you the achievement, try putting 2499 chips instead. Thanks to DiatomicMaster for the info.
Additionnal Info: Gentleman's Attire is an outfit available to be worn by John Marston found in Red Dead Redemption.
To receive in on Xbox 360. Go to the pause menu, scroll down to Social Club. Then click on the "Y" button to "Sign In". You then enter your E-mail address, and a new password. Then the Gentlemen's Attire will be in your game.http://reddead.wikia.com/wiki/Gentleman%27s_Attire
Thanks to Deviousapple for the info