Chlorine will leave tap water if you give it some time, it would leave tap water faster than oxygen or carbon dioxide. That wont kill your fish, the chlorine is already gone hopefully, unless it bound with something.
Some people actually have really good tap water and run FO tanks just fine. I would not panic or anything. I would be hesitant to do a 100% water change, it is not that dire. If you have the ability to run some carbon that will help helpful.
If you are really worried I would get some large jugs and fill up some water from Kroger. They have a RO machine near the veggies. I ran my 55g reef on that for months when I first started and did not have a RO unit.
Call Russ at buckeye field supply and buy a 75 GPD premium RO/DI unit. Or, simply ask him what you should get based on your needs. They are local and have great customer service.
When you get the unit follow all of the instructions, there are a few complicated things to do but its not too bad. You do not want to shock anything so I would start out with a 25% water change. Maybe a 50% depending on how things are looking.
It sounds like you just set up this tank so it will have a massive algae bloom and need to cycle. Do you have a protein skimmer set up? Its not required at first but it is really helpful to have one. I would do some research on "cycling a tank" and "protein skimmers".
In order of importance (assuming you have a light and flow (powerheads).
1. RO/DI unit
2. Refractometer
3. Protein skimmer