Chessboard style for a table with CSS. How?

I have the following table and I want to make it to look like a chessboard. How can I do it? I tried with nth-child, but I couldn't solve it. Thank you for any help!

<table class="chess">
        <tr>
            <td> </td>
            <td>Brasov</td>
            <td>Zarnesti</td>       
        </tr>

        <tr>
            <td> R14701 </td>
            <td> 06:06 </td>
            <td> 06:57 </td>
        </tr>

        <tr>
            <td> R14705 </td>
            <td> 08:10 </td>
            <td> 08:59 </td>
        </tr>

        <tr>
            <td> R14709 </td>
            <td> 12:10 </td>
            <td> 12:59 </td>
        </tr>

        <tr>
            <td> R14713 </td>
            <td> 14:10 </td>
            <td> 14:59 </td>
        </tr>
    </table>

I tried this, but something is wrong,

td:nth-child(even) {
    background: grey;
}

td:nth-child(odd){
    background: white;
}

tr:nth-child(even){
    background:white;
}

tr:nth-child(odd){
        background: grey;
}