Check constraint to require one of two columns
Expanding on ypercube's question comments:

The first thing you need to do is make the securityID column nullable:

ALTER TABLE dbo.Employee
ALTER COLUMN securityID nvarchar(50) NULL;


Then the required check constraint is quite straightforward:

ALTER TABLE dbo.Employee
ADD CONSTRAINT [CK dbo.Employee securityID or alternateID must not be NULL]
CHECK (securityID IS NOT NULL OR alternateID IS NOT NULL);


Regarding the 'friendly' name I chose for the check constraint, see:

Naming CHECK and UNIQUE Constraints by Greg Low.