Delete rows older than x days without locking table

we have a quite big MS SQL database with millions of rows. I created a simple script to delete rows older than 1 month, but this seems to lock the table and creates trouble for the application. The table has an indexed "ID" PK, and also a "date" column which I will use for this task. What is the best way to do this without causing the lock? I was considering partitioning, but not sure if its the best way to go. Thanks in advance.