I was able to recreate this problem.
CREATE DATABASE Archive
PRIMARY ( NAME = Arch1,
FILENAME = 'c:\data\archdat1.mdf'),
FILEGROUP FileStreamGroup1 CONTAINS FILESTREAM( NAME = Arch3,
FILENAME = 'c:\data\filestream1')
LOG ON ( NAME = Archlog1,
FILENAME = 'c:\data\archlog1.ldf')
CREATE TABLE Archive.dbo.Records
[Id] [uniqueidentifier] ROWGUIDCOL NOT NULL UNIQUE,
[Chart] VARBINARY(MAX) FILESTREAM NULL
ALTER TABLE Archive.dbo.Records WITH NOCHECK
ADD CONSTRAINT testfilestream UNIQUE (ID)
ALTER TABLE Archive.dbo.Records
DROP CONSTRAINT testfilestream
Best I can tell this is a bug and (1) SQL Server has a hard rule relating to tables with FILESTREAM columns that says "if they try to drop ANY UNIQUE constraint on the ROWGUIDCOL column in a table with FILESTREAM, don't let them" and/or (2) There only ever is one UNIQUE constraint on a column and making another is like making an alias. So when you try and drop one, you're really dropping both.
As to how to solve it. Unfortunately, you can't add a second ROWGUIDCOL type column to a table, so that prevents a fix that's internal to the existing table. You'll probably have to create a new table with the same schema, (minus the extra unique constraint), copy the data from the current table to the new table, then drop the old table and rename the new one back to the old name.