Copper, or Aluminum wiring on that branch circuit? 
That is quite scary. You need to find that connection, because it is hanging by a thread. Find out where power enters the circuit. It may be at the light box itself. A temperature change or mouse running across the wire could have made the connection. That is a fire waiting to happen. Loose connections can get very hot.Thank you all for responding. Three of the four outlets were replaced yesterday. Only the lamp outlet remains to be replaced. After cycling the breaker the outlets were still dead. Each outlet read 0VAC with the breaker off and .2VAC with the breaker on. The breaker was left on overnight and this afternoon the outlets suddenly came on. Nothing was done. One outlet is occupied by a clock, which alerted me to it being on. I tested the other outlets and all are functional except the lamp outlet, which has not been replaced. Turning on the lamp switch does not effect the other outlets. What would cause the change? Thanks.
Well....what does that tell you? :jester:When the light switch was turned on, the circuit failed again.
So, you're saying that you had oxidation on the breaker contacts?I replaced all outlets on the circuit using screw terminals. Two had evidence of arcing at the pushpin connections. When I turned the breaker on, the circuit was still dead. In checking the breaker later, I mistakingly threw the adjacent breaker, which caused the problem circuit to come on! I turned the mains off and removed and replaced the breaker on the problem circuit several times and reconnected its wire. The mains were turned on and all is well. Many thanks to you all.