Gigabit Ethernet over multimode fiber is supported only over limited distances. I would recommend installing single mode fiber if that's possible, and using 1000BASE-LX optics. Otherwise, 100-megabit Fast Ethernet is probably the best you can get out of that length of multimode, as ScottMac said.
If you use 1000BASE-SX short wavelength optics over 62.5µm multimode, the maximum supported link length is 220m to 275m, depending on the modal bandwidth of the fiber.
If you use 1000BASE-LX long wavelength optics over 62.5µm multimode, the maximum specified link length is 550m. And you need mode conditioning patch cables to provide an offset launch of the LX signal into the multimode fiber.
Having said that, I think it may be possible for you to push Gigabit Ethernet out to 1km over 62.5 multimode. I have read that even worst-case multimode fiber links can support LX out to 700m, and that the distance was reduced to 550m to agree with the ISO/IEC 11801 structured cabling model. So, if you don't have worst-case fiber you might be able to do this. But it really, really, really depends on knowing the exact manufacturer and product number of your fiber, in order to determine what it's capable of. Testing the fiber with an OTDR wouldn't hurt, either.
As far as equipment is concerned, your best chances to go from a copper (RJ-45) Gigabit port across your 1km of multimode fiber to an SX fiber (SC) Gigabit port on the other side, would be with two different media converters. One that converts from 1000BASE-T to 1000BASE-LX; and the other that converts from 1000BASE-LX back to 1000BASE-SX. Use mode conditioning patch cables on the LX ports, and a regular multimode patch cable on the SX port.
Transition Networks www.transition.com is another manufacturer of media converters worth checking out. I have used theirs on a number of occasions, with good results.
Hope this helps.
