From the UCSC download site:

curl -s "http://hgdownload.cse.ucsc.edu/goldenPath/hg19/database/snp132.txt.gz" |\
gunzip -c |\
cut -d '       ' -f 2,3,4,5
chr1    10326   10327   rs112750067
chr1    10433   10433   rs56289060
chr1    10439   10440   rs112155239
chr1    10439   10440   rs112766696
chr1    10468   10469   rs117577454
chr1    10491   10492   rs55998931
chr1    10518   10519   rs62636508
chr1    10532   10533   rs114315702
chr1    10582   10583   rs58108140
chr1    10827   10828   rs10218492

You can get this in simple table format from UCSC. http://hgdownload.cse.ucsc.edu/goldenPath/hg19/database/snp132.txt.gz

Or from their mysql:

mysql --user=genome --host=genome-mysql.cse.ucsc.edu -NA \
    -e "select chrom, chromStart, chromEnd, name from hg19.snp132" hg19 > snp132.hg19.txt

It looks as if the table SNPChrPosOnRef stores that piece of information. The database dumps can be downloaded from the dbSNP ftp server.