I found this paper from the Journal of the American Association of Pediatrics
"Results. Among varicella cases reported to the surveillance project, 4.5% of cases in 1995 and 13.3% of cases in 1999 reported previous varicella. More than 95% of first infections were physician diagnosed, epidemiologically linked to another case, or had a rash description consistent with varicella; the same was true for reported second infections. People who reported reinfections were generally healthy. There was a family history of repeat infections in 45% of people who reported reinfections.
Conclusions. Clinical varicella reinfections may occur more commonly than previously thought. Additional studies of the predictive value of a positive varicella history and laboratory studies of reported reinfections are indicated to guide varicella vaccination policy."
This is a much higher number than I was expecting.