Why didn't the U-2 spyplane have any chaff?
There are two main reasons for this:


USAF and CIA believed that the Russians (or anyone else) wouldn't be able to shoot down aircraft operating at (>60000ft).
Most of the aircraft operating during that time did not have chaff dispensers to deploy chaff as needed. For that to work, the pilot has to either visually acquire the missile or have a RWR, which became widely used only in the later stages of Vietnam War.


Another important reason is tactics. The chaff was not used in WWII in a tactical capacity i.e. to protect individual fighters, but to provide blanket coverage to bomber fleets. This practice continued well into the Vietnam War. For example, specialized aircraft (usually fighters) will dump chaff to provide a 'corridor' for following bombers. For an aircraft on reconnaissance mission, this is as good as advertising its presence. 

A lot of aircraft in that era went without any countermeasures. For example, the English Electric Lightning carried no chaffs till its retirement in 80's.