Even though there is no default option to hide the RememberMe checkbox from the pre-chat form, you are able to hide it using Custom CSS. To do so, navigate to Configuration > Chat > Chat buttons > Edit your chat button.
In the Pre-chat form > Design tab scroll down to the "Custom CSS" section and add the following CSS code:
#rememberMePanel {
display: none !important;
}
Do not forget to APPLY the CSS code and SAVE the form.