Tenant complains of rodents - who pays for pest control?

[Kevin Thomas]

We bought a duplex and several months later an existing tenant is complaining about rodents.  I contacted a local pest control company and they want $100 to start and $45 per month for both units and a 1 year contract.  My lease is vague about who pays for this but it seems to fall on the landlord since the landlord is obligated to keep the place habitable.  

My thought was to explain to the complaining tenant that I will take care of the cost of the service for the first year.  

How would other seasoned landlords handle this? 

Thank you!!