Fridays Ltd, which produces thousands of free range eggs in Cranbrook, wants to expand its operation in Horsmonden.
Residents fear the extra traffic and noise from the 32-hectare site will have a detrimental impact on the area.
The company said it was responding to a 5% year-on-year increase in demand for free range eggs.
The family-run business is one of the three biggest egg producers and packers in the country.
If agreed, its new chicken farm would be located at Pullens Farm, in Lamberhurst Road, which is on the outskirts of the village of Horsmonden.
Resident Sarah Overton said: "The sheer scale of this development is extraordinary.
"We're talking the equivalent of 80 football pitches, 64,000 birds at any one time producing 360,000 eggs a week, using mechanical processes and only needing one full-time person to look after them, and three part-time egg collectors.
"It equates to industrialisation in the countryside, which is bad enough, but this is industrialisation of an area of outstanding natural beauty with protected species that we all need to be careful to preserve," she said.
Fridays Ltd has lodged its application with Tunbridge Wells Borough Council, with a provisional decision expected in August.
Horsmonden Parish Council is discussing the plans on Monday.

Bellusci, 27, spent the 2016-17 season with Empoli in Italy's Serie A and has a year left on his contract at Leeds.
Empoli were relegated to Serie B, but the Italian centre-back is seeking a transfer to stay in his home country, with Bologna rumoured to be interested.
He joined the Whites from Catania in August 2014 and has scored two goals in 61 appearances for the club.
Plans by a company that wants to put 64,000 chickens on an area of outstanding natural beauty in Kent have been met with anger by local residents.
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Leeds defender Giuseppe Bellusci will not return to the club following a loan spell with Empoli, BBC Leeds reports.