Here's an example from this blog post:
fetch('/big-data.csv').then(function(response) {
  var reader = response.body.getReader();
  var partialCell = '';
  var returnNextCell = false;
  var returnCellAfter = "Jake";
  var decoder = new TextDecoder();
  function search() {
    return reader.read().then(function(result) {
      partialCell += decoder.decode(result.value || new Uint8Array, {
        stream: !result.done
      });
      // Split what we have into CSV 'cells'
      var cellBoundry = /(?:,|\r\n)/;
      var completeCells = partialCell.split(cellBoundry);
      if (!result.done) {
        // Last cell is likely incomplete
        // Keep hold of it for next time
        partialCell = completeCells[completeCells.length - 1];
        // Remove it from our complete cells
        completeCells = completeCells.slice(0, -1);
      }
      for (var cell of completeCells) {
        cell = cell.trim();
        if (returnNextCell) {
          reader.cancel("No more reading needed.");
          return cell;
        }
        if (cell === returnCellAfter) {
          returnNextCell = true;
        }
      }
      if (result.done) {
        throw Error("Could not find value after " + returnCellAfter);
      }
      return search();
    })
  }
  return search();
}).then(function(result) {
  console.log("Got the result! It's '" + result + "'");
}).catch(function(err) {
  console.log(err.message);
});
Note that streaming responses aren't supported yet in all browsers, check the compatibility table on MDN.