If this is an alias you're using outside of an event it will be $1 and not $nick.
This works fine here if I'm using /dcc_chk nick
Code:
alias dcc_chk {
  if $chat($1) { echo -a Open already }
  else dcc chat $1
}


So does this if it is called from an event.
Code:
alias dcc_chk {
  if $chat($nick) { echo -a Open already }
  else dcc chat $nick
}