Legal Question in Landlord & Tenant Law in Illinois

From your zip code it appears the unit is in Chicago, so I will answer using Chicago law (Chicago has much better laws for tenants than other municipalities).

Under the Chicago RLTO, which applies to almost all apartments in the city, a landlord can enter the unit upon 2 days notice (no notice needed in emergencies) for legitimate reasons. Showing the unit to buyers is a legitimate reason, but the frequency cannot be so often as to harass the tenants. Moreover, unless you consent, the access should only take place between 8 am and 8 pm.

Hosting an open house in your unit does not seem reasonable and I would ask for compensation, the landlord may be willing to work with you.

If you are interested in reading about the many rights and remedies tenants in Chicago have, I have written an article on the topic here: http://bc-firm.com/tenants-rights-chicago/

I agree w/ Mr. Brabender, but you should also check your lease. If the lease was made at a time when the landlord was thinking about selling the building, there may be a section or clause about it in the lease, that may still be legal under the RLTO but potentially create some issues for you.