If just one ATI Radeon HD 4870 video card, then the Corsair CX400 with 30 amps on the 12 volt rail will do. The official recommendation is for a 450 watt power supply.
The ATI Radeon HD 4870 video cards require two 75 watt, 6 pin, PCI-e power connections. The Corsair CX400 and VX450 power supplies only come with one 6 pin PCI-epower cable. That's typical for low wattage psu's. That is not adisaster. I know the XFX version of the 4870 video card ships with a molex to 6 pin adapter. Many brands usually include a molex to 6 pin adapter just in case.
Here is a link to a power consumption chart from a Tom's Hardware review of the 4870:http://www.tomshardware.com/reviews/radeon-hd-4870,1964-15.html
The blue color is the test system total power consumption while playing Test Drive Unlimited. It weighed in at 283 watts. Peak during a stress test would have been much higher.