Kaiwa's Answer will have the effect of changing the rest of the string to lower case, this might not be the behaviour you want.
Regular Expressions[
^] are a good way to go about what you want:
string regularExpressionPattern = "zzz"
Regex regex = new Regex(regularExpressionPattern, RegexOptions.IgnoreCase);
string foo = "zZz this is sample text";
string bar = regex.Replace(foo, "Goodbye");
Note that my code just replaces "zzz", ignoring the case. If you want you replace the
first word (rather than just "hello") you can create a regular expression to do this. Obviously, in either case, you'll need to work out the pattern for yourself :-).