Desktop
You can stop chat requests by going to your messaging settings page and adjusting who can send chat requests to "nobody."
iOS
You can turn notifications off for Chat in your settings.
Open up your profile (upper left) > Click "Settings" (bottom left) > Click username for account settings (top) > Manage notifications > Toggle off chat requests and chat messages.
Android
You can turn notifications off for Chat in your settings.
Open up your profile (upper left) > Click "Settings" (gear icon - bottom) > Account settings (top) > Manage notifications > Toggle off chat requests and chat messages.