Even though there is no default option to hide the customer´s initial message sent by the system if a pre-chat form is used, you are able to hide it using Custom CSS. To do so, navigate to Configuration > Chat > Chat buttons > Edit your chat button.
In the "Chat window" tab scroll down to the "Custom CSS" section and add the following CSS code:
.MessageNotificationTypeZ, .chatMessagesGroup-My:first-of-type {
display: none !important;
}
Do not forget to APPLY the CSS code and SAVE the chat window.