Although not perfect, the best I came up with was to set the zero point to 0.0001 and then set the y-axis min to 0.0001:
yAxis: {
min:0.0001,
type: 'logarithmic'
},
series: [{
data: [100,10,0.0001,0.1,0.01,0.1]
}]
Also, this answer may nelp: Highcharts - best way to handle and display zero (or negative) values in a line chart series with logarithmic Y axis