Chrome doesn't respect the Windows setting for zone identifiers and has no inbuilt option to deactivate them. There are a few alternatives though:
Global attachment policy
You can change how Windows handles zone identifiers using the group policy editor (gpedit.msc); the location of these settings is User Configuration -> Administrative Templates -> Windows Components -> Attachment Manager.
Do not preserve zone information in file attachments has no effect on Chrome (see Issue 5719), but changing the default risk of attachments* to low will deactivate the dialog completely and ignore a file's zone security information.
Additionally, you can specify exceptions for certain file extension to, for example, always ask when opening downloaded .exe files.
Delete zone settings from the command line
If you only want to remove the zone settings from certain files, you can use streams.exe from the Sysinternals Suite to delete all alternate NTFS data streams:
streams -d <file> and
streams -s -d <directory>
:Zone.Identifier is the stream used to store zone security information.
Sources
chromium - Issue 5719: SetInternetZoneIdentifier does not respect the SaveZoneInformation policy
msigeek.com - How to Remove Security Warning Message – Files Downloaded from Internet