If you have dogs there is a dog cab service that charges $25. I have two dogs so I never really thought about using it. Luckily my dogs are good with my bike when I need to take them to the vet. Don't know if this is worth checking out http://chicago.outugo.com/services/pet-taxi/
and searching the internet found this site--- seems a bit expensive but depending on where you need to go.My vet is only a mile so I dont mind walking or biking, but good to know for an emergency. http://www.chicagopettransport.com/Services.html
Thank you for the ideas. I ended up using Pet in Transport and the service was excellent and I was happy to be able to get my sick dog to the vet so she can start feeling better! I failed to mention my dog is 75+lbs...so a carrier is never a possibility! Thanks again. I highly recommend Pet in Transport if ever in need.