Similar, although not the same component, the [lightning:pill][1] supports adding icons within it:

    <lightning:pill label="Pill Label">
        <aura:set attribute="media">
            <lightning:icon iconName="standard:account"  alternativeText="Account"/>
        </aura:set>
    </lightning:pill>

some styling is needed to hide the remove option though:

    .THIS .slds-pill__remove{
        display:none;
    }

Otherwise, you will have to tweak the [SLDS Badge Blueprint][2] - similar to what @codeyinthecloud posted.


  [1]: https://developer.salesforce.com/docs/component-library/bundle/lightning:pill/example#lightningcomponentdemo:examplePillIcon
  [2]: https://www.lightningdesignsystem.com/components/badges/