Yes. Maybe. But why?

If the nonprofit produces a play but doesn’t charge people to attend, it will not be conducting a trade or business and will have no unrelated business income.  Gifts that the audience members give without being required to do so will be considered contributions.  The charity will want to acknowledge the gifts and advise the donors they did not receive goods or services in return for the payment.  (See Ready Reference Page: “IRS Requires Substantiation of Contributions”)

If the charity produces the play and charges attendees, it will be carrying on an unrelated trade or business, but it may not generate unrelated business taxable income unless it is considered “regularly carried on.”  Two or three performances once a year would not be considered regularly carried on.  If it runs for the length of time a Broadway show would run, it is likely to be considered regularly carried on and subject to unrelated business income tax (“UBIT”).  If it is unrelated business income, the charity can deduct reasonable expenses incurred in producing the income.  If the organization receives more than $1000 in gross unrelated business taxable income, it will have to recognize the amount on its Form 990 tax information return.  If it receives more than $1000 net unrelated business taxable income, it will have to pay tax. (See Ready Reference Page: “Nonprofits Often Worry About UBIT”)

The real question, however, is why the charity would spend its time doing things unrelated to its mission.  It might make sense as an annual fundraiser.  But if there is a substantive reason for producing a play other than making extra money, could it be a play related to the organization’s charitable purpose?  Or could the organization expand its charitable purpose to include the educational ideas included in the play?  It would probably make a lot more sense to charge everybody who wants to attend a play that produces related fee for service income (where you could also ask for additional contributions for support) than to spend the time and energy to produce a play that might — and might not — generate some contributions.