What does happen when you get two identical dates?

As you don't say anything about the context, supposing unix-like, I thought I could mention various one-liners to get a feeling of your data:

% steph@apexPDell2 (/home/stephan/t) %
% cat data.txt # I added the last line                                
+                                       

item  group  entry_date
34     gr1    2003-03-02
12     gr1    1990-03-14
39     gr3    2002-04-11
66     gr4    2006-03-16
32     gr3    1998-02-13
90     gr1    2004-06-15
55     gr4    1999-06-15
10     gr1    2003-03-02

% steph@apexPDell2 (/home/stephan/t) %
% LC_ALL=C sort -k 3 data.txt | perl -lna -e 'print if $F[1] eq q{gr1}
+ and $F[0] == 34'
34     gr1    2003-03-02

% steph@apexPDell2 (/home/stephan/t) %
% sort -k 3 data.txt | grep gr1 | sort -n | head -n1
10     gr1    2003-03-02
[download]

The last one reads as sort on the date, select group gr1, select on the first numerically and keep tghe first line. In this particular case it is faster to grep first.