Select observations from a subset to create a new

I have a dataset (Purchase.df) that contains many columns and rows. The important variable names for this question are "Customer", "OrderDate", "DateRank" (which ranks the dates so I can find the smallest date) and "BrandName." Below is a very small sample of what I'm working with: (I'm new to this website, so I hope what I paste below works)

Purchase.df<-structure(list(Customer = c(10071535L, 10071535L, 10071535L, 
10071535L, 10071535L, 10071535L, 10071711L, 10071711L, 10071711L, 
10071711L, 10071711L, 10071711L, 10071711L, 10071711L, 10071711L, 
10071711L, 10071711L, 10071711L, 10072059L, 10072059L, 10072059L, 
10072113L, 10072113L, 10072113L, 10072113L, 10072113L, 10072113L, 
10072113L), BrandName = structure(c(1L, 2L, 2L, 2L, 3L, 3L, 2L, 
2L, 2L, 2L, 3L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 
2L, 3L, 3L, 3L, 3L), .Label = c("X", "Y", "Z"), class = "factor"), 
OrderDate = structure(c(14L, 14L, 15L, 16L, 19L, 20L, 11L, 
18L, 5L, 6L, 1L, 17L, 21L, 22L, 23L, 8L, 10L, 13L, 7L, 9L, 
12L, 4L, 4L, 2L, 2L, 2L, 3L, 3L), .Label = c("1/17/2011 0:00", 
"1/19/2010 0:00", "1/25/2010 0:00", "1/4/2010 0:00", "10/22/2010 0:00", 
"11/15/2010 0:00", "11/23/2011 0:00", "12/14/2011 0:00", 
"12/16/2011 0:00", "2/7/2012 0:00", "3/16/2010 0:00", "3/21/2012 0:00", 
"4/16/2012 0:00", "4/27/2012 0:00", "5/16/2012 0:00", "5/30/2012 0:00", 
"5/5/2011 0:00", "6/1/2010 0:00", "6/12/2012 0:00", "7/3/2012 0:00", 
"8/1/2011 0:00", "8/16/2011 0:00", "9/19/2011 0:00"), class = "factor"), 
DateRank = c(18.5, 18.5, 20, 21, 24, 25, 15, 23, 9, 10, 1, 
22, 26, 27, 28, 12, 14, 17, 11, 13, 16, 7.5, 7.5, 3, 3, 3, 
5.5, 5.5)), .Names = c("Customer", "BrandName", "OrderDate", 
"DateRank"), row.names = c(NA, -28L), class = "data.frame")

I've created a subset of this large dataset (subset.df) which finds the first OrderDate for each customer, and tells me which brand they purchased. I used the following code to do this:

subset1<-split(Purchase.df,Purchase.df$Customer)
subset2<-lapply(split(Purchase.df,Purchase.df$Customer), function(chunk) chunk[which(chunk$DateRank==min(chunk$DateRank)),])
subset.df<-do.call(rbind, as.list(subset2))

Now, I want to figure out which customers ordered Brand X on their first OrderDate, and create a new dataset (BigSubset.df) that contains all of the OrderDates for the customers that purchased Brand X on their first order date.

Should look something like this:

Customer    BrandName   OrderDate   DateRank
10071535    X   4/27/2012 0:00  18.5
10071535    Y   4/27/2012 0:00  18.5
10071535    Y   5/16/2012 0:00  20
10071535    Y   5/30/2012 0:00  21
10071535    Z   6/12/2012 0:00  24
10071535    Z   7/3/2012 0:00   25
10072059    X   11/23/2011 0:00 11
10072059    X   12/16/2011 0:00 13
10072059    X   3/21/2012 0:00  16
10072113    X   1/4/2010 0:00   7.5
10072113    Y   1/4/2010 0:00   7.5
10072113    Y   1/19/2010 0:00  3
10072113    Z   1/19/2010 0:00  3
10072113    Z   1/19/2010 0:00  3
10072113    Z   1/25/2010 0:00  5.5
10072113    Z   1/25/2010 0:00  5.5

I can't seem to get R to reference the smaller dataset when I attempt to create BigSubset.df from Purchase.df because the number of rows are not equal. I've searched on Google and haven't seen any answers, so I'm not even sure if this is possible in R. Let me know what you think.

Maybe I'm misunderstanding, but I believe this works:

Xfirst <- as.vector(subset.df[subset.df$BrandName == "X", ])$Customer
BigSubset.df <- Purchase.df[Purchase.df$Customer %in% Xfirst, ]

I think you may have a bug in your daterank because in your example Customer 10072113 has date 1/19/2010 ranked 3 but the earlier 1/4/2010 ranked 7.5. (Sidenote, in your chunk function you can use which.min(chunk$DateRank) instead of which(chunk$DateRank==min(chunk$DateRank)), which I believe is more efficient.)