<p>I am currently working for a company that has a website running mysql/php (all tables are also using the MYISAM table type).</p>

<p>We would like to implement replication, but I have read in the mysql docs and elsewhere on the internet that this will lock the tables when doing the writes to the binary log (which the slave dbs will eventually read from).</p>

<p>Will these locks cause a problem on a live site that is fairly write-heavy?  Also, is there a way to enable replication without having to lock the tables?</p>

If you change your table types to innodb, row level locking is used.  Also, your replication will be more stable, as updates will be transactional.  MyISAM replication is a long-term pain.
Be sure that your servers are version-matched, and ALWAYS be sure to shut down the master before shutting down the slaves.  You can bring the master up again immediately after shutting down the slaves, but you do have to take it down.
Also, make sure you use appropriate autoextend options for InnoDB.  And, while you're at it, you'll probably want to migrate away from float and double to 'decimal' (which means mysql 5.1.)  That will save you some replication headaches.
That's probably a bit more than you asked for.  Enjoy.
P.s., yes the myisam locks can cause problems.  Also, innodb is slower than myisam, unless myisam is blocking for a huge select.