* {
    font-family:sans-serif;
}
body {
    text-align:center;
    padding:1em;
}
.messages {
    width:100%;
    max-width:700px;
    text-align:left;
    display:inline-block;
}
.messages img {
    background-color:rgb(248,244,240);
    width:36px;
    height:36px;
    border-radius:0.2em;
    display:inline-block;
    vertical-align:top;
    margin-right:0.65em;
}
.messages .time {
    display:inline-block;
    color:rgb(200,200,200);
    margin-left:0.5em;
}
.messages .username {
    display:inline-block;
    font-weight:600;
    line-height:1;
}
.messages .message {
    display:inline-block;
    vertical-align:top;
    line-height:1;
    width:calc(100% - 3em);
}
.messages .message .msg {
    line-height:1.5;
}

* {
    font-family: sans-serif;
}

body {
    text-align: center;
    padding: 1em;
}

.messages {
    width: 100%;
    max-width: 700px;
    text-align: left;
    display: inline-block;
}

.messages img {
    background-color: rgb(248, 244, 240);
    width: 36px;
    height: 36px;
    border-radius: 0.2em;
    display: inline-block;
    vertical-align: top;
    margin-right: 0.65em;
    float: left;
}

.messages .time {
    display: inline-block;
    color: rgb(200, 200, 200);
    margin-left: 0.5em;
}

.messages .username {
    display: inline-block;
    font-weight: 600;
    line-height: 1;
}

.messages .message {
    display: inline-block;
    vertical-align: top;
    line-height: 1;
    width: calc(100% - 3em);
}

.messages .message .msg {
    line-height: 1.5;
}

Add float:left on img; reformat CSS
Add float:left on img; reformat CSS
