I have a (large) bgzipped VCF file. I would like to read through it by chunks of records (say, 1000), doing something on these, and saving them back to another bgzipped VCF file.

Following the examples at the bottom of ?TabixFile and ?readVCF, here is what I'm doing for the moment:

library(VariantAnnotation)
tabix.file <- TabixFile(file="input.vcf.gz", yieldSize=1000)
open(tabix.file)
con <- file("output.vcf", open="a")
while(nrow(vcf <- readVcf(tabix.file, "mygenome"))){
    ... # do something on the "vcf" object
    writeVcf(obj=vcf, filename=con)
}
close(con)
close(tabix.file)
bgzip("output.vcf")
indexTabix("output.vcf.bgz", "vcf")

It doesn't seem very efficient to first append iteratively to an uncompressed file, and then to compress it. But is there a way to directly append to a bgzipped VCF file? Or maybe there is a completely different way?

In theory, one could use a gzfile()  in append mode to add gzip-compressed blocks to the file (assuming a bgzip is essentially a set of concatenated gzip files, which I think it is). You would need to pass index=FALSE to writeVcf() and index explicitly when finished.