Indexing nvarchar(128) in SQL Server Have no idea how indexing works in SQL Server.

Working with a SQL Server 2012 Intel Xeon 2.2 GHz dual core 8 GB RAM. 

Will indexing a nvarchar(128) in addition to int primary key cause any performance issue for a 1000 row table which has a nvarchar(max) as one of its columns? 

This will be part of website that gets average 3000 hits a day.
When considering the impact of new index, the important things to think are how often rows are added to the table, is the indexed field getting updated (often) and how many distinct values there are in that field (selectivity).

For table this size, it's probably not going improve the performance that much, but if you're getting deadlocks it might help. 

If you create the index, after it you can monitor the impact from "Index Usage Statistics" -report in SSMS:

http://blog.sqlauthority.com/2014/09/19/sql-server-ssms-index-usage-statistics-physical-statistics-user-statistics/

From there you can see the number of times it's being used (scans &amp; seeks) and the number of times it was needed to update.