I think that you need to register your non standard class using setOldclass
first.
require(chron)
dts <- dates(c("05/20/13", "06/10/13"))
tms <- times(c("19:30:00", "22:30:05"))
setOldClass("chron")
newclass <- setRefClass("newclass",
fields = list(time = "chron"))
mydate <- newclass(time = chron(dates = dts, times = tms))
mydate$time
## [1] (05/20/13 19:30:00) (06/10/13 22:30:05)