The following code does that:
import scala.util.parsing.combinator.Parsers
import scala.util.parsing.input.{Position, Reader}
object Main {
  def main(args: Array[String]): Unit = CVParser("one\ntwo\nthree")
}
object CVParser {
  def apply(in: String): Any = impl.parse(in)
  private object impl extends Parsers {
    override type Elem = String
    def parse(in: String): ParseResult[String~String~String] = {
      val reader = new ByLineReader(in.split(System.lineSeparator).toList, 1)
      grammar(reader)
    }
    // private
    private val grammar = SampleParser ~ SampleParser ~ SampleParser
    private class ByLineReader(lines: List[String], lineNo: Int) extends Reader[String] {
      override def first: String = lines.headOption getOrElse ""
      override def rest: Reader[String] =
        if (!lines.isEmpty) new ByLineReader(lines.tail, lineNo + 1)
        else new ByLineReader(lines, lineNo)
      override def pos: Position = new Position {
        def line: Int = lineNo
        def column: Int = 0
        def lineContents: String = first
      }
      override def atEnd: Boolean = lines.size == 1
    }
    private object SampleParser extends Parser[String] {
      def apply(in: Input): ParseResult[String] = {
        println(in.first + "\n---------")
        Success(in.first, in.rest)
      }
    }
  }
}
Outputs:
one
---------
two
---------
three
---------
Now new parsers which accept a line of text may be written and combined using usual parser combinators, like ~, ~>, <~, |, rep, etc.