George did not allow Lennie to carry his own what in the first chapter? no
Work card. George was sure Lennie would lose it.
George didn't let Lennie carry a lot of things. One thing he didn't let Lennie carry were the business cards because he knew Lennie would lose them.
He also didn't let Lennie carry a mouse. George just said that it was unnecessary for him to carry one, especially if it's dead. He was also worried that Lennie might scare away other people again with the dead mouse.