As the other answers here state, starting with no equipment changes some of the premises of the game, which should be accounted for. However, as you didn't ask about that, let's dive in to your question:
Option 1: Each character begin play with minimal equipment
As Hey I can Chan commented, some classes will be seriously hampered without their class' "signature tool of the trade" - a cleric without his holy symbol cannot cast spells or turn undead, a wizard without his spellbook is limited to casting the spells he happened to memorize and can't prepare them again, and - as in your case - a fighter built around a specific weapon will be hampered without it.
You can resolve this by allowing each character to have a single/few items which will make the difference between being almost useless and just barely equipped. You can even have that equipment to be of poor quality, to make gaining 'proper' items a priority (such as a rusty weapon with -1 to attacks/damage, or a spellbook salvaged from a fire so that it has no/few blank pages for adding spells).
Option 2: Start with nothing, gain the basics fast
I've once ran a campaign where the PCs started as captives of a gnoll tribe - all their equipment taken, they were caged, guarded, and would either become slaves or dinner if they didn't work together to break out quickly - the players really enjoyed fighting their way out with sticks and bones as weapons, and managed to reclaim some of their equipment (the wizard got his book easily as the gnolls didn't want it, the paladin had the satisfaction of taking his sword back from a slain guard...). Planned correctly, you can either allow your PCs to gain the basic equipment they need, or reclaim their own equipment back (allowing them to still have an ancestral weapon or specifically tailored gear).
Granted, this isn't the usual way a campaign starts, but it can be extremely satisfying.
Specifically, your fighter may find some length of chain (maybe he is even chained at the beginning) and use it as a poor spiked chain. You can treat it as the standard weapon, or downgrade it (-1 for attacks, deal bludgeoning damage - possibly less than the regular weapon, be heavier, easier to break etc.). This can even be the narrative reason for the fighter to adopt the chain as his main weapon later on. Alternatively, just have one of the first foes or treasures have a spiked chain. Unlike a wizard without his spellbook, a level 1 fighter with a stick can still handle combat pretty well...
At any rate, starting with no equipment will make the first encounters much tougher, probably deadly - unless you adjust them accordingly - it's probably good to discuss this with the players and make sure you are all on the same page.