According to the documentation all values resulting from parsing the CSV will be strings:

Note that the values themselves are always strings; they will not be automatically converted to numbers.

You will have to specify an accessor function which takes care of the conversion

d3.csv('Book1.csv', convert, init); //load data, convert, then initialize chart



function convert(d) {

  return {

    date: new Date(d.date),

    value: +d.value         // convert string to number

  };

} 

As a side-effect this will also simplify your code because it frees you from having to do a conversion every time you access the values. Here is the full code:

var Chart = (function(window, d3) {



  var svg, data, x, y, xAxis, yAxis, dim, chartWrapper, line, path, margin = {},

    width, height;



  d3.csv('Book1.csv', convert, init); //load data, convert, then initialize chart



  function convert(d) {

    return {

      date: new Date(d.date),

      value: +d.value         // convert string to number

    };

  } 



  //called once the data is loaded

  function init(csv) {

    data = csv;



    //initialize scales

    xExtent = d3.extent(data, function(d, i) {

      return d.date;

    });

    yExtent = d3.extent(data, function(d, i) {

      return d.value;

    });

    x = d3.time.scale().domain(xExtent);

    y = d3.scale.linear().domain(yExtent);



    //initialize axis

    xAxis = d3.svg.axis().orient('bottom');

    yAxis = d3.svg.axis().orient('left');



    //the path generator for the line chart

    line = d3.svg.line()

      .x(function(d) {

        return x(d.date)

      })

      .y(function(d) {

        return y(d.value)

      });



    //initialize svg

    svg = d3.select('#chart').append('svg');

    chartWrapper = svg.append('g');

    path = chartWrapper.append('path').datum(data).classed('line', true);

    chartWrapper.append('g').classed('x axis', true);

    chartWrapper.append('g').classed('y axis', true);



    //render the chart

    render();

  }



  function render() {



    //get dimensions based on window size

    updateDimensions(window.innerWidth);



    //update x and y scales to new dimensions

    x.range([0, width]);

    y.range([height, 0]);



    //update svg elements to new dimensions

    svg

      .attr('width', width + margin.right + margin.left)

      .attr('height', height + margin.top + margin.bottom);

    chartWrapper.attr('transform', 'translate(' + margin.left + ',' + margin.top + ')');



    //update the axis and line

    xAxis.scale(x);

    yAxis.scale(y);



    svg.select('.x.axis')

      .attr('transform', 'translate(0,' + height + ')')

      .call(xAxis);



    svg.select('.y.axis')

      .call(yAxis);



    path.attr('d', line);

  }



  function updateDimensions(winWidth) {

    margin.top = 20;

    margin.right = 50;

    margin.left = 50;

    margin.bottom = 50;



    width = winWidth - margin.left - margin.right;

    height = 500 - margin.top - margin.bottom;

  }



  return {

    render: render

  }

})(window, d3);