Yes, and that would not be currency. It might be useful to think of this as a tiered system.
‘Trade’ is a top-level idea, an exchange between entities. On a tier below that, i.e. a closer specification of ‘trade’, exists ‘barter’ (trading goods for other goods or services) and ‘money’ (trading some representational, notional item for goods/services). ‘Chickens’ as a payment is a further specification of bartering, while ‘currency’ is a further specification of ‘money’ (being ‘money’ defined/in use by a specific power/state).