Yes, you can transfer money from an annuity to pay long-term-care premiums without owing taxes. This was the result of a tax break that was included in the Pension Protection Act of 2006. Kimberly Lankford posted an article called ‘Use Annuities to Pay for Long-Term Care’ which gives great insight into the advantages that this tax break creates. She gives some powerful examples on how this can be used to both provide themselves with long-term-care while decreasing their taxable gains.
For the specifics, please read the full article linked here. Please note that there are many variables to when evaluating this arrangement, so be sure to consult with a retirement income specialist. Many new annuity products have been brought to the market since this article was posted, so be sure that you get current expert advice to properly evaluate the best alternatives.