deafpanzer
I would order an aluminum barrel if I was you... Tamiya kit barrel may come in two pieces and it is pain in butt to make it look good.
The barrel does indeed come in two halves. There is a little trick to this barrel, as the mouldings incorporate the breech as well. This means that if you retrofit an aluminium barrel, you need to get the correct length, as the full length barrel passes through the mantlet. Do not buy a barrel which ends at the sleeve on the mantlet, unless you intend to do a little surgery.
Aber make a number of KwK39 L/60 barrels, but most are for Dragon kits with a different barrel mounting. If looking at Aber, look for part # 35L-33, which is intended for the Tamiya kit.
RB Model also has a barrel which appears to be suitable, 35B104
In both cases, the kit barrel is cut off at the breech and the replacement glued in its place.
There may be other barrels available, but I know that the two I have listed should fit the Tamiya kit.
Armorscale also do a KwK39/L60 including a resin mantlet, but it is overkill for this kit, with the applique armour mounted over the mantlet making it rather pointless. (Might be good for earlier versions (Late H/J?) with the L/60 without applique armour)
EDIT: Look for the March 2007 issue of FSM, which contains an article demonstrating some simple upgrades to this kit using a metal barrel and the Eduard "zoom" PE set.