Additional chips can be obtained from the Cashier Services booth on the casino floor, where you can also collect a visitor bonus once per day which is currently set to 1000 free chips.
When you first arrive in the casino, you'll get the option to purchase a Standard Membership from the Guest Services desk near the entrance or by following the on-screen prompt, which costs GTA$500 but gives you 5000 GTA Online casino chips to get started.
