The implementation looks like this:

    def step(taken: ByteString)(input: Input): (Iteratee[ByteString], Input) = input match {
      case Chunk(more) ⇒
        val bytes = taken ++ more
        val startIdx = bytes.indexOfSlice(delimiter, math.max(taken.length - delimiter.length, 0))
        if (startIdx >= 0) {
          val endIdx = startIdx + delimiter.length
          (Done(bytes take (if (inclusive) endIdx else startIdx)), Chunk(bytes drop endIdx))
        } else {
          (Next(step(bytes)), Chunk.empty)
        }
      case EOF              ⇒ (Failure(new EOFException("Unexpected EOF")), EOF)
      case e @ Error(cause) ⇒ (Failure(cause), e)
    }

The offending line are these:

        
        val bytes = taken ++ more
        val startIdx = bytes.indexOfSlice(delimiter, math.max(taken.length - delimiter.length, 0))

So unfortunately we rescan the whole aggregated bytes variable for every new chunk.