It looks like you don't have the horizontal X axis labels defined properly in the chart series. The dates start at 1/1/1900 because that's the date you would get from a cell value of 1, which is what Excel will plot when the x-axis is left blank. There's a couple ways to check this.
Right click on the chart series, choose 'Select Data...'. In the chart data range box at the top of the window, does the range displayed in the box include the date values? Also, in the box in the lower right, are the values dates or just numeric 1,2,3....? These are indications that the series does not include the date labels.
You can also click the chart series and look in the formula bar below the ribbon.
The formula string should look something like this:
The top string includes an additional series parameter that identifies the X-axis labels.
To resolve, right click on the series, choose 'Select Data...'. Click the series name in the box on the lower left, then click the 'Edit' button above the box on the right. Select the range of dates excluding the header cell.