The pilot initially called ATS after becoming airborne, having tried unsuccessfully to make radio contact on the ground during taxi. An airport groundsman was asked to maintain a sarwatch for the aircraft until the pilot reported that he had made contact with ATS. The pilot was instructed to remain OCTA until radar identified, due to crossing traffic. When the transponder was first observed the aircraft was at FL105 on climb. The CTA lower limit in the area is 4,500 ft. No breakdown in separation occurred. After checking the terminal chart on taxi the pilots were satisfied that the controlled airspace started at FL200 on their route. After the mistake was revealed the pilots accepted responsibility for the error, citing lack of familiarity with the area, the light blue ink on the chart and relatively poor cockpit lighting as factors.