Why does the U-2 use a chase car when landing?
It is to help the pilot land the aircraft (the chase cars are also used during takeoff). The U2 is considered notoriously difficult to fly in low altitudes- a tradeoff in an aircraft optimized for very high altitude flight:

Because the U-2 was so specialized, it was amazingly difficult to fly. ... the lower the U-2 flew, the heavier its unassisted controls got, to the point where pilots literally had to brute-force the plane around during take-off and landing.
... landings were the biggest problem. The replacement for Johnson's cart-and-skid ground system was a compact setup — two centrally located landing gear in the fuselage and one detachable &quot;pogo&quot; gear on each wing — that turned the U-2 into little more than a 30,000-pound bicycle. Because of the high-lift wings, pilots didn't so much land the plane as fly it really close to the ground (usually about two feet), stall it, and then fall out of the sky.

The decreased visibility of the pilots, combined with the highly efficient wings and bicycle landing gear meant that unassisted landings are difficult (but certainly possible, as has been demonstrated)- thus the chase cars.
On of the chase car drivers (themselves U2 pilots) describes the drill:

... the objective is ensuring that the pilot safely landing the aircraft... calling him down to two feet... holding them off there and then the plane will just kind of settle down on the ground.