use strict;
my $a='ABCAAAABBBCCCCCAAABBBCCC';
my $b='ASRGRTGRT89579843rrrrrr';
print '$a matches',$/ if $a =~ /^[ABC]+$/;
print '$b matches',$/ if $b =~ /^[ABC]+$/;
[download]

Update: The regex is anchored at the beginning and end of the string, and requires 1 or more of character class [ABC].

perl -MYAPE::Regex::Explain -e 'print YAPE::Regex::Explain->new(qr/^[A
+BC]+$/)->explain;'
The regular expression:

(?-imsx:^[ABC]+$)

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  ^                        the beginning of the string
----------------------------------------------------------------------
  [ABC]+                   any character of: 'A', 'B', 'C' (1 or more
                           times (matching the most amount possible))
----------------------------------------------------------------------
  $                        before an optional \n, and the end of the
                           string
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
[download]

Update2:

Of course, this is not at all efficient, checking every character in the string to ensure it is one that you want. The responses below are much more efficient.