From the description of your data, it sounds like you may be dealing with FASTA format. Even if you're not, the following technique (with a little modification) may do what you want.

#!/usr/bin/env perl

use strict;
use warnings;

while (<DATA>) {
    if (/^>/) {
        print "\n" unless $. == 1;
        print;
    }
    else {
        chomp;
        print;
    }
}

print "\n";

__DATA__
>chunk1
c1_line1
c1_line2
c1_line3
>chunk2
c2_line1
c2_line2
c2_line3
[download]

Output:

>chunk1
c1_line1c1_line2c1_line3
>chunk2
c2_line1c2_line2c2_line3
[download]

Use Benchmark, to compare this with any other solutions, to determine which runs the fastest.

For the split and join (or .=) operations you mention, I'd have to guess you're using some form of 'local $/ = ...' (see perlvar: Variables related to filehandles) — I'd need more information to comment further on that. Of course, there's no reason why you can't compare those options with any others.

Two comments regarding stripping embedded newlines from a string using "s/\n//g/":

1. That's incorrect syntax. There's no slash after the modifier (i.e. it's just s/\n//g). See perlop: Regexp Quote-Like Operators.
2. Transliteration (e.g. y/\n//d) is probably faster. See perlop: Quote-Like Operators. [Note: y/// and tr/// are synonymous.]

If my guess at your requirements is wrong, please supply more information to help us help you. The guidelines in "How do I post a question effectively?" should point you in the right direction with respect to this.