Something too highly regarded to be open to criticism or curtailment.
Origin
This term is an allusion to the Hindu reverence for cows. The first use in English that I have found of the term 'sacred cow' as a description of the recipient of that long-standing Hindu veneration is in an American newspaper from the 1850s. This is a reprint of a letter that was sent by Wady Jahed, an Indian emigre, living in Janesville, Wisconsin, to The Calcutta Times. Mr Jahed sent the letter on the'17th day of the 6th Moon' and The Janesville Free Press printed it in January 1854:
To the most eminent Kaali Ramon, High Brahmin, at Benares, India.
The religion of the Hindoo is now well established here, but I find many things to correct. For instance the grain which they bring as an offering to the goddess Bhavani, which they pronounce brewery, they work up into a liquor which they drink in honor of the gods, instead of feeding it to the sacred bulls and cows; they also eat the flesh of animals, and do other vile things.
Kiss the sacred cow for me, and may Doorgha bless you at all times.
From your Slave,
WADY JAHED.
It seems he was right to question the lack of knowledge of sacred cows in the USA at the time. Several other US newspapers refer to them in the late 19th century and variously describe them as coming from India, Tibet and 'Muhammedan lands'.
The figurative use of the term 'sacred cow', to refer to a project or process that is immune from tampering, is American in origin and also dates from the late 19th century. A piece in The New York Herald, in March 1890, uses a simile that comes close to that metaphorical use:
"While the great ditch may be regarded as one of the commercial diversities of the commonwealth, to worship it as a sort of sacred cow is not necessarily a work of true statesmanship."
In September 1909 The Galveston Daily News went a little further and referred to a project that was a 'sacred cow', rather than merely being like one:
"They understand Mr. Bryan's position to be one of antagonism to the contention that raw material is a 'sacred cow,' immune from tariff reform, ever to be upon the dutiable list and in consequence enjoying the blessings of incidental protection."