You can do this in base R without installing any external packages.
Assuming that the βDateβ column has a Date class, we take the βDateβ diff and based on whether the difference between neighboring elements is more than 1 or not, we can create a grouping index ('indx') by taking the total amount ( cumsum ) logical vector.
indx <- cumsum(c(TRUE,abs(diff(df1$Date))>1))
In the second stage, we can use ave with "indx" as a grouping vector and take diff of ch. The length of the diff output will be 1 less than the length of the "ch" column. Therefore, we can add NA to make the lengths the same.
ave(df1$ch, indx, FUN=function(x) c(diff(x),NA))
data
df1 <- structure(list(Date = structure(c(15706, 15707, 15708, 15709, 15715, 15716, 15762, 15763, 15764, 12116), class = "Date"), ch = c(12L, 23L, 4L, 78L, 120L, 94L, 36L, 2L, 41L, 22L)), .Names = c("Date", "ch"), row.names = c(NA, -10L), class = "data.frame")