The fast food firm said that it had a new "delivery partner", but that "teething problems" meant hundreds of its restaurants UK-wide had been affected by a shortage of the meat.
While some restaurants were closed completely, others have been forced to operate a limited menu or shorter opening times.
A spokesman for the firm said: "The chicken crossed the road, just not to our restaurants. We’ve brought a new delivery partner on board, but they’ve had a couple of teething problems - getting fresh chicken out to 900 restaurants across the country is pretty complex.
“We won’t compromise on quality, so no deliveries has meant some of our restaurants are closed, and others are operating a limited menu, or shortened hours. “Shout out to our restaurant teams who are working flat out to get us back up and running again.”
Only 21 of its 53 restaurants in Scotland are listed as open on the company's website in the wake of the delivery problem.
The store has published a list of the outlets which are now open - comprising around 260 of the chain's 900 restaurants.
KFC last week switched its delivery contract to DHL from South African-owned distribution group Bidvest.
DHL said: "Due to operational issues, a number of deliveries in recent days have been incomplete or delayed. We are working with our partners to rectify the situation as a priority and apologise for any inconvenience."
Chicken lovers took to Twitter to express their dismay, while some went as far as to contact their MP to complain about the closures.
@shafiqlatif wrote: "Just went to the Meadowbank Edinburgh branch for some hot bites and they're shut due to lack of chicken. When did kfc ever run out of chicken??"
William Wadsworth added: “I’ve wanted KFC for 3 days and there has been no chicken at any of them I have been to in Manchester is this the end of the world or has someone in finance not paid the bill?????”
London MP Neil Coyle said: "I've been contacted by disappointed #KFC customers on Borough High St #SE1 & Walworth Rd #SE17 today."
DHL announced in November that it had been appointed alongside QSL to manage the supply and distribution of food products and packaging for around 900 KFC restaurants throughout the UK. It is thought that Bidvest had previously held the contract for almost a decade.
The statement said that DHL would manage the physical warehouse and distribution service, with KFC adding it had specifically chosen the pair for their reputation of “innovation in logistics” across other industries.
Mick Rix, GMB National Officer said that Bidvest had had a network of distribution centres across the UK - while DHL have just one. He said: “We tried to warn KFC this decision would have consequences – well now the chickens are coming home to roost.”
KFC is the world’s second-largest restaurant chain by sales after McDonald’s - with almost 20,000 locations globally in 123 countries.
The Scottish KFC outlets affected by closure
• Heathfield Retail Park, Heathfield Road, Ayr, KA8 9SS
• Showcase Leisure Park, Langmuir Road, Bargeddie, G69 7TU
• Braehead, Braille Crescent, Renfrew, PA4 0DJ
• Braehead Shopping Centre, Kings Inch Road, Glasgow, G51 4BN
• Coatbank Street, Coatbridge, ML5 3SP
• South Muirhead Road, Cumbernauld, G67 1AX
• St James Retail Park, Glasgow Road, Dumbarton, G82 1RB
• Cuckoo Bridge Retail Park, Glasgow Road, Dumfries, DG2 9BF
• Callender Road, Falkirk, FK1 1SY
• Hermiston Place, Glasgow, G32 0LU
• Pollokshaws Road, Glasgow, G41 1PS
• Renfield Street, Glasgow, G2 1NH
• Ashenyards Park, Kilwinning, KA20 3EG
• Queens Drive Retail Park, Queens Drive, Kilmarnock, KA1 3XB
• Renfield Street, Renfrew, PA4 8RF
• Dalmarnock Road, Rutherglen, G73 1NY
• Kerse Road, Stirling, FK7 7NU