I took a continuing education class to acquire new skills, can I claim a deduction for the cost of the class?

Yes, if the new skills improve your performance in your current trade or business, the associated costs are deductible as an Employee Business Expense on Schedule A - Itemized Deductions.

The position of the IRS on this matter appears below, taken from IRS Pub. 529 Miscellaneous Deductions.

"Work-Related Education

You can deduct expenses you have for education, even if the education may lead to a degree, if the education meets at least one of the following two tests.

It maintains or improves skills required in your present work.

It is required by your employer or the law to keep your salary, status, or job, and the requirement serves a business purpose of your employer.

You can't deduct expenses you have for education, even though one or both of the preceding tests are met, if the education:

Is needed to meet the minimum educational requirements to qualify you in your trade or business, or

Is part of a program of study that will lead to qualifying you in a new trade or business.

If your education qualifies, you can deduct expenses for tuition, books, supplies, laboratory fees, and similar items, and certain transportation costs.

If the education qualifies you for a new trade or business, you can't deduct the educational expenses even if you don’t intend to enter that trade or business."